Kovalnogov, V. N.; Fedorov, R. V.; Karpukhina, M. T.; Kornilova, M. I.; Simos, T. E.; Tsitouras, Ch. Economical handling of Runge-Kutta-Nyström step rejection. (English) Zbl 1522.65123 J. Comput. Appl. Math. 438, Article ID 115528, 9 p. (2024). MSC: 65L06 65L05 PDFBibTeX XMLCite \textit{V. N. Kovalnogov} et al., J. Comput. Appl. Math. 438, Article ID 115528, 9 p. (2024; Zbl 1522.65123) Full Text: DOI
Amirali, Ilhame; Acar, Hülya Stability inequalities and numerical solution for neutral Volterra delay integro-differential equation. (English) Zbl 1522.65252 J. Comput. Appl. Math. 436, Article ID 115343, 11 p. (2024). MSC: 65R20 45D05 45J05 PDFBibTeX XMLCite \textit{I. Amirali} and \textit{H. Acar}, J. Comput. Appl. Math. 436, Article ID 115343, 11 p. (2024; Zbl 1522.65252) Full Text: DOI
Montijano, J. I.; Rández, L.; Calvo, M. Explicit Runge-Kutta methods for the numerical solution of linear inhomogeneous IVPs. (English) Zbl 1522.65126 J. Comput. Appl. Math. 425, Article ID 115083, 17 p. (2023). MSC: 65L06 65L05 PDFBibTeX XMLCite \textit{J. I. Montijano} et al., J. Comput. Appl. Math. 425, Article ID 115083, 17 p. (2023; Zbl 1522.65126) Full Text: DOI
Preuss, Adam; Lipoth, Jessica; Spiteri, Raymond J. When and how to split? A comparison of two IMEX splitting techniques for solving advection-diffusion-reaction equations. (English) Zbl 1490.65133 J. Comput. Appl. Math. 414, Article ID 114418, 18 p. (2022). MSC: 65L04 65L05 65L06 65M20 65Y20 PDFBibTeX XMLCite \textit{A. Preuss} et al., J. Comput. Appl. Math. 414, Article ID 114418, 18 p. (2022; Zbl 1490.65133) Full Text: DOI
Simos, T. E.; Tsitouras, Ch. On high order Runge-Kutta-Nyström pairs. (English) Zbl 1482.65110 J. Comput. Appl. Math. 400, Article ID 113753, 10 p. (2022). MSC: 65L05 65L06 PDFBibTeX XMLCite \textit{T. E. Simos} and \textit{Ch. Tsitouras}, J. Comput. Appl. Math. 400, Article ID 113753, 10 p. (2022; Zbl 1482.65110) Full Text: DOI
Okor, T.; Nwachukwu, G. C. High order extended boundary value methods for the solution of stiff systems of ODEs. (English) Zbl 1482.65103 J. Comput. Appl. Math. 400, Article ID 113750, 20 p. (2022). MSC: 65L04 65L05 65L06 65L20 PDFBibTeX XMLCite \textit{T. Okor} and \textit{G. C. Nwachukwu}, J. Comput. Appl. Math. 400, Article ID 113750, 20 p. (2022; Zbl 1482.65103) Full Text: DOI
D’Ambrosio, Raffaele; Paternoster, Beatrice Multivalue collocation methods free from order reduction. (English) Zbl 1458.65073 J. Comput. Appl. Math. 387, Article ID 112515, 12 p. (2021). MSC: 65L04 65L60 PDFBibTeX XMLCite \textit{R. D'Ambrosio} and \textit{B. Paternoster}, J. Comput. Appl. Math. 387, Article ID 112515, 12 p. (2021; Zbl 1458.65073) Full Text: DOI
Moradi, A.; Farzi, J.; Abdi, A. Order conditions for second derivative general linear methods. (English) Zbl 1458.65088 J. Comput. Appl. Math. 387, Article ID 112488, 17 p. (2021). MSC: 65L06 PDFBibTeX XMLCite \textit{A. Moradi} et al., J. Comput. Appl. Math. 387, Article ID 112488, 17 p. (2021; Zbl 1458.65088) Full Text: DOI
Yan, Xiaoqiang; Zhang, Chengjian Numerical approximation to a class of nonlinear hybrid system with distributed delay via block boundary value methods. (English) Zbl 1524.65987 J. Comput. Appl. Math. 378, Article ID 112942, 13 p. (2020). MSC: 65R20 45J05 65L05 65L06 65L20 PDFBibTeX XMLCite \textit{X. Yan} and \textit{C. Zhang}, J. Comput. Appl. Math. 378, Article ID 112942, 13 p. (2020; Zbl 1524.65987) Full Text: DOI
Ernsthausen, John M.; Nedialkov, Nedialko S. Stepsize selection in the rigorous defect control of Taylor series methods. (English) Zbl 1429.65145 J. Comput. Appl. Math. 368, Article ID 112483, 10 p. (2020). MSC: 65L05 34A34 41A58 65G20 65G40 41A10 PDFBibTeX XMLCite \textit{J. M. Ernsthausen} and \textit{N. S. Nedialkov}, J. Comput. Appl. Math. 368, Article ID 112483, 10 p. (2020; Zbl 1429.65145) Full Text: DOI
Akhtari, Bahar Numerical treatment of stochastic delay differential equations: a global error bound. (English) Zbl 1416.65025 J. Comput. Appl. Math. 361, 249-270 (2019). MSC: 65C30 60H10 34K50 60H35 PDFBibTeX XMLCite \textit{B. Akhtari}, J. Comput. Appl. Math. 361, 249--270 (2019; Zbl 1416.65025) Full Text: DOI
Abdi, A.; Hosseini, S. A.; Podhaisky, H. Adaptive linear barycentric rational finite differences method for stiff ODEs. (English) Zbl 1503.65141 J. Comput. Appl. Math. 357, 204-214 (2019). MSC: 65L04 65L05 65L06 65L12 65D05 65L20 PDFBibTeX XMLCite \textit{A. Abdi} et al., J. Comput. Appl. Math. 357, 204--214 (2019; Zbl 1503.65141) Full Text: DOI
Yapman, Ömer; Amiraliyev, Gabil M.; Amirali, Ilhame Convergence analysis of fitted numerical method for a singularly perturbed nonlinear Volterra integro-differential equation with delay. (English) Zbl 1415.65170 J. Comput. Appl. Math. 355, 301-309 (2019). MSC: 65L11 65L12 65L20 65R20 PDFBibTeX XMLCite \textit{Ö. Yapman} et al., J. Comput. Appl. Math. 355, 301--309 (2019; Zbl 1415.65170) Full Text: DOI
Kulikov, G. Yu.; Weiner, R. Doubly quasi-consistent fixed-stepsize numerical integration of stiff ordinary differential equations with implicit two-step peer methods. (English) Zbl 1435.65102 J. Comput. Appl. Math. 340, 256-275 (2018). MSC: 65L04 65L20 65L70 PDFBibTeX XMLCite \textit{G. Yu. Kulikov} and \textit{R. Weiner}, J. Comput. Appl. Math. 340, 256--275 (2018; Zbl 1435.65102) Full Text: DOI
Constantinescu, Emil M. Generalizing global error estimation for ordinary differential equations by using coupled time-stepping methods. (English) Zbl 1377.65088 J. Comput. Appl. Math. 332, 140-158 (2018). MSC: 65L06 65L70 34A34 65L05 PDFBibTeX XMLCite \textit{E. M. Constantinescu}, J. Comput. Appl. Math. 332, 140--158 (2018; Zbl 1377.65088) Full Text: DOI Link
Hosseini Nasab, M.; Abdi, A.; Hojjati, G. Symmetric second derivative integration methods. (English) Zbl 1376.65148 J. Comput. Appl. Math. 330, 618-629 (2018). MSC: 65P10 65L06 37M15 PDFBibTeX XMLCite \textit{M. Hosseini Nasab} et al., J. Comput. Appl. Math. 330, 618--629 (2018; Zbl 1376.65148) Full Text: DOI
Soleimani, Behnam; Weiner, Rüdiger A class of implicit peer methods for stiff systems. (English) Zbl 1372.65198 J. Comput. Appl. Math. 316, 358-368 (2017). MSC: 65L04 65L05 65L20 PDFBibTeX XMLCite \textit{B. Soleimani} and \textit{R. Weiner}, J. Comput. Appl. Math. 316, 358--368 (2017; Zbl 1372.65198) Full Text: DOI
Schmitt, Bernhard A.; Weiner, Rüdiger Efficient A-stable peer two-step methods. (English) Zbl 1372.65197 J. Comput. Appl. Math. 316, 319-329 (2017). MSC: 65L04 65L20 PDFBibTeX XMLCite \textit{B. A. Schmitt} and \textit{R. Weiner}, J. Comput. Appl. Math. 316, 319--329 (2017; Zbl 1372.65197) Full Text: DOI
Wen, Liping; Zhou, Yan Convergence of one-leg methods for neutral delay integro-differential equations. (English) Zbl 1357.65326 J. Comput. Appl. Math. 317, 432-446 (2017). MSC: 65R20 45J05 45G10 PDFBibTeX XMLCite \textit{L. Wen} and \textit{Y. Zhou}, J. Comput. Appl. Math. 317, 432--446 (2017; Zbl 1357.65326) Full Text: DOI
Hosseini Nasab, M.; Hojjati, G.; Abdi, A. G-symplectic second derivative general linear methods for Hamiltonian problems. (English) Zbl 1353.65133 J. Comput. Appl. Math. 313, 486-498 (2017). MSC: 65P10 37M15 PDFBibTeX XMLCite \textit{M. Hosseini Nasab} et al., J. Comput. Appl. Math. 313, 486--498 (2017; Zbl 1353.65133) Full Text: DOI
Wang, Wansheng Uniform ultimate boundedness of numerical solutions to nonlinear neutral delay differential equations. (English) Zbl 1352.65174 J. Comput. Appl. Math. 309, 132-144 (2017). MSC: 65L03 34K28 34K40 65L06 65L20 PDFBibTeX XMLCite \textit{W. Wang}, J. Comput. Appl. Math. 309, 132--144 (2017; Zbl 1352.65174) Full Text: DOI
Kudu, Mustafa; Amirali, Ilhame; Amiraliyev, Gabil M. A finite-difference method for a singularly perturbed delay integro-differential equation. (English) Zbl 1346.65076 J. Comput. Appl. Math. 308, 379-390 (2016). MSC: 65R20 45D05 45A05 45J05 PDFBibTeX XMLCite \textit{M. Kudu} et al., J. Comput. Appl. Math. 308, 379--390 (2016; Zbl 1346.65076) Full Text: DOI
Abdi, A. Construction of high-order quadratically stable second-derivative general linear methods for the numerical integration of stiff ODEs. (English) Zbl 1382.65190 J. Comput. Appl. Math. 303, 218-228 (2016). MSC: 65L04 65L20 PDFBibTeX XMLCite \textit{A. Abdi}, J. Comput. Appl. Math. 303, 218--228 (2016; Zbl 1382.65190) Full Text: DOI
Weng, Peter Chang-Yi; Phoa, Frederick Kin Hing Small-sample statistical condition estimation of large-scale generalized eigenvalue problems. (English) Zbl 1332.65061 J. Comput. Appl. Math. 298, 24-39 (2016). MSC: 65F35 15A12 65F15 65F50 15A24 62F10 PDFBibTeX XMLCite \textit{P. C. Y. Weng} and \textit{F. K. H. Phoa}, J. Comput. Appl. Math. 298, 24--39 (2016; Zbl 1332.65061) Full Text: DOI
Weiner, R.; Kulikov, G. Yu. Local and global error estimation and control within explicit two-step peer triples. (English) Zbl 1301.65067 J. Comput. Appl. Math. 262, 261-270 (2014). MSC: 65L05 65L06 65L20 65L50 65L70 PDFBibTeX XMLCite \textit{R. Weiner} and \textit{G. Yu. Kulikov}, J. Comput. Appl. Math. 262, 261--270 (2014; Zbl 1301.65067) Full Text: DOI
Mustapha, Kassem; Ryan, Jennifer K. Post-processing discontinuous Galerkin solutions to Volterra integro-differential equations: analysis and simulations. (English) Zbl 1291.65387 J. Comput. Appl. Math. 253, 89-103 (2013). MSC: 65R20 45D05 45J05 45E10 PDFBibTeX XMLCite \textit{K. Mustapha} and \textit{J. K. Ryan}, J. Comput. Appl. Math. 253, 89--103 (2013; Zbl 1291.65387) Full Text: DOI
Dieci, Luca; Lopez, Luciano A survey of numerical methods for IVPs of ODEs with discontinuous right-hand side. (English) Zbl 1246.65111 J. Comput. Appl. Math. 236, No. 16, 3967-3991 (2012). MSC: 65L05 34A34 65-02 PDFBibTeX XMLCite \textit{L. Dieci} and \textit{L. Lopez}, J. Comput. Appl. Math. 236, No. 16, 3967--3991 (2012; Zbl 1246.65111) Full Text: DOI
Cong, Nguyen Huu; Thuy, Nguyen Thu Two-step-by-two-step PIRK-type PC methods based on Gauss-Legendre collocation points. (English) Zbl 1230.65084 J. Comput. Appl. Math. 236, No. 2, 225-233 (2011). Reviewer: M. Gousidou-Koutita (Thessaloniki) MSC: 65L06 65L05 34A34 65Y05 65L20 PDFBibTeX XMLCite \textit{N. H. Cong} and \textit{N. T. Thuy}, J. Comput. Appl. Math. 236, No. 2, 225--233 (2011; Zbl 1230.65084) Full Text: DOI
París, A.; Rández, L. New embedded explicit pairs of exponentially fitted Runge-Kutta methods. (English) Zbl 1189.65144 J. Comput. Appl. Math. 234, No. 3, 767-776 (2010). MSC: 65L06 PDFBibTeX XMLCite \textit{A. París} and \textit{L. Rández}, J. Comput. Appl. Math. 234, No. 3, 767--776 (2010; Zbl 1189.65144) Full Text: DOI
Nguyen-Ba, Truong; Bozic, Vladan; Kengne, Emmanuel; Vaillancourt, Rémi A one-step 7-stage Hermite-Birkhoff-Taylor ODE solver of order 11. (English) Zbl 1188.65097 J. Comput. Appl. Math. 234, No. 1, 192-208 (2010). MSC: 65L06 65D05 34A34 65L20 PDFBibTeX XMLCite \textit{T. Nguyen-Ba} et al., J. Comput. Appl. Math. 234, No. 1, 192--208 (2010; Zbl 1188.65097) Full Text: DOI
Wang, Wansheng; Wen, Liping; Li, Shoufu Stability of linear multistep methods for nonlinear neutral delay differential equations in Banach space. (English) Zbl 1202.65103 J. Comput. Appl. Math. 233, No. 10, 2423-2437 (2010). Reviewer: Thomas Sonar (Braunschweig) MSC: 65L20 65L06 65L50 35K40 34K30 34G20 65L03 PDFBibTeX XMLCite \textit{W. Wang} et al., J. Comput. Appl. Math. 233, No. 10, 2423--2437 (2010; Zbl 1202.65103) Full Text: DOI
Benner, Peter; Li, Ren-Cang; Truhar, Ninoslav On the ADI method for Sylvester equations. (English) Zbl 1176.65050 J. Comput. Appl. Math. 233, No. 4, 1035-1045 (2009). MSC: 65F30 15A24 40C05 37L99 PDFBibTeX XMLCite \textit{P. Benner} et al., J. Comput. Appl. Math. 233, No. 4, 1035--1045 (2009; Zbl 1176.65050) Full Text: DOI
Bellen, Alfredo; Guglielmi, Nicola Solving neutral delay differential equations with state-dependent delays. (English) Zbl 1166.65034 J. Comput. Appl. Math. 229, No. 2, 350-362 (2009). MSC: 65L05 34K13 34K18 34K28 34K40 PDFBibTeX XMLCite \textit{A. Bellen} and \textit{N. Guglielmi}, J. Comput. Appl. Math. 229, No. 2, 350--362 (2009; Zbl 1166.65034) Full Text: DOI
Prentice, J. S. C. General error propagation in the RK\(r\)GL\(m\) method. (English) Zbl 1168.65036 J. Comput. Appl. Math. 228, No. 1, 344-354 (2009). Reviewer: Manuel Calvo (Zaragoza) MSC: 65L05 65L70 65L06 34A34 65L50 PDFBibTeX XMLCite \textit{J. S. C. Prentice}, J. Comput. Appl. Math. 228, No. 1, 344--354 (2009; Zbl 1168.65036) Full Text: DOI
Nguyen-Ba, Truong; Sharp, Philip W.; Vaillancourt, Rémi Hermite-Birkhoff-Obrechkoff four-stage four-step ODE solver of order 14 with quantized step size. (English) Zbl 1153.65071 J. Comput. Appl. Math. 222, No. 2, 608-621 (2008). MSC: 65L06 65L05 34A34 68W30 65L50 65L70 PDFBibTeX XMLCite \textit{T. Nguyen-Ba} et al., J. Comput. Appl. Math. 222, No. 2, 608--621 (2008; Zbl 1153.65071) Full Text: DOI
Cong, Nguyen Huu; Xuan, Le Ngoc Twostep-by-twostep PIRK-type PC methods with continuous output formulas. (English) Zbl 1156.65070 J. Comput. Appl. Math. 221, No. 1, 165-173 (2008). Reviewer: Thomas Rauber (Bayreuth) MSC: 65L06 65L05 65Y05 34A34 PDFBibTeX XMLCite \textit{N. H. Cong} and \textit{L. N. Xuan}, J. Comput. Appl. Math. 221, No. 1, 165--173 (2008; Zbl 1156.65070) Full Text: DOI
Calvo, M.; González-Pinto, S.; Montijano, J. I. Global error estimation based on the tolerance proportionality for some adaptive Runge-Kutta codes. (English) Zbl 1149.65052 J. Comput. Appl. Math. 218, No. 2, 329-341 (2008). Reviewer: M. Gousidou-Koutita (Thessaloniki) MSC: 65L05 65L06 65L70 PDFBibTeX XMLCite \textit{M. Calvo} et al., J. Comput. Appl. Math. 218, No. 2, 329--341 (2008; Zbl 1149.65052) Full Text: DOI
Prentice, J. S. C. The RKGL method for the numerical solution of initial-value problems. (English) Zbl 1135.65348 J. Comput. Appl. Math. 213, No. 2, 477-487 (2008). MSC: 65L06 65L05 65L20 65L70 34A34 PDFBibTeX XMLCite \textit{J. S. C. Prentice}, J. Comput. Appl. Math. 213, No. 2, 477--487 (2008; Zbl 1135.65348) Full Text: DOI
Finden, W. F. An error term and uniqueness for Hermite-Birkhoff interpolation involving only function values and/or first derivative values. (English) Zbl 1134.65012 J. Comput. Appl. Math. 212, No. 1, 1-15 (2008). MSC: 65D05 41A10 PDFBibTeX XMLCite \textit{W. F. Finden}, J. Comput. Appl. Math. 212, No. 1, 1--15 (2008; Zbl 1134.65012) Full Text: DOI
Finden, W. F. Higher order approximations using interpolation applied to collocation solutions of two-point boundary value problems. (English) Zbl 1131.65063 J. Comput. Appl. Math. 206, No. 1, 99-115 (2007). Reviewer: Johannes Schropp (Konstanz) MSC: 65L10 65L60 65L70 34B05 PDFBibTeX XMLCite \textit{W. F. Finden}, J. Comput. Appl. Math. 206, No. 1, 99--115 (2007; Zbl 1131.65063) Full Text: DOI
Shampine, L. F. Design of software for ODEs. (English) Zbl 1116.65085 J. Comput. Appl. Math. 205, No. 2, 901-911 (2007). MSC: 65L05 65L10 65Y15 34K28 PDFBibTeX XMLCite \textit{L. F. Shampine}, J. Comput. Appl. Math. 205, No. 2, 901--911 (2007; Zbl 1116.65085) Full Text: DOI
Jannelli, Alessandra; Fazio, Riccardo Adaptive stiff solvers at low accuracy and complexity. (English) Zbl 1089.65061 J. Comput. Appl. Math. 191, No. 2, 246-258 (2006). MSC: 65L05 34A34 65L50 65Y20 65L70 PDFBibTeX XMLCite \textit{A. Jannelli} and \textit{R. Fazio}, J. Comput. Appl. Math. 191, No. 2, 246--258 (2006; Zbl 1089.65061) Full Text: DOI
Verner, J. H. Starting methods for two-step Runge-Kutta methods of stage-order 3 and order 6. (English) Zbl 1079.65078 J. Comput. Appl. Math. 185, No. 2, 292-307 (2006). MSC: 65L05 65L06 65L20 34A34 PDFBibTeX XMLCite \textit{J. H. Verner}, J. Comput. Appl. Math. 185, No. 2, 292--307 (2006; Zbl 1079.65078) Full Text: DOI
Guglielmi, Nicola Open issues in devising software for the numerical solution of implicit delay differential equations. (English) Zbl 1079.65076 J. Comput. Appl. Math. 185, No. 2, 261-277 (2006). MSC: 65L05 65L70 34K28 65L06 PDFBibTeX XMLCite \textit{N. Guglielmi}, J. Comput. Appl. Math. 185, No. 2, 261--277 (2006; Zbl 1079.65076) Full Text: DOI
Söderlind, Gustaf; Wang, Lina Evaluating numerical ODE/DAE methods, algorithms and software. (English) Zbl 1081.65533 J. Comput. Appl. Math. 185, No. 2, 244-260 (2006). MSC: 65L80 65L05 34A34 34A09 65Y15 68N01 PDFBibTeX XMLCite \textit{G. Söderlind} and \textit{L. Wang}, J. Comput. Appl. Math. 185, No. 2, 244--260 (2006; Zbl 1081.65533) Full Text: DOI
Cash, J. R.; Mazzia, F.; Sumarti, N.; Trigiante, D. The role of conditioning in mesh selection algorithms for first order systems of linear two point boundary value problems. (English) Zbl 1077.65084 J. Comput. Appl. Math. 185, No. 2, 212-224 (2006). MSC: 65L10 34B15 65L50 65L70 PDFBibTeX XMLCite \textit{J. R. Cash} et al., J. Comput. Appl. Math. 185, No. 2, 212--224 (2006; Zbl 1077.65084) Full Text: DOI
Krogh, Fred T. On developing mathematical software. (English) Zbl 1101.68113 J. Comput. Appl. Math. 185, No. 2, 196-202 (2006). MSC: 68W30 PDFBibTeX XMLCite \textit{F. T. Krogh}, J. Comput. Appl. Math. 185, No. 2, 196--202 (2006; Zbl 1101.68113) Full Text: DOI
Hamdi, S.; Enright, W. H.; Ouellet, Y.; Schiesser, W. E. Method of lines solutions of the extended Boussinesq equations. (English) Zbl 1077.65104 J. Comput. Appl. Math. 183, No. 2, 327-342 (2005). MSC: 65M20 35K55 35Q35 PDFBibTeX XMLCite \textit{S. Hamdi} et al., J. Comput. Appl. Math. 183, No. 2, 327--342 (2005; Zbl 1077.65104) Full Text: DOI
Cash, J. R.; Mazzia, F. A new mesh selection algorithm, based on conditioning, for two-point boundary value codes. (English) Zbl 1076.65065 J. Comput. Appl. Math. 184, No. 2, 362-381 (2005). MSC: 65L10 65L50 34B15 65L70 PDFBibTeX XMLCite \textit{J. R. Cash} and \textit{F. Mazzia}, J. Comput. Appl. Math. 184, No. 2, 362--381 (2005; Zbl 1076.65065) Full Text: DOI
González-Pinto, S.; Rojas-Bello, R. Speeding up Newton-type iterations for stiff problems. (English) Zbl 1072.65100 J. Comput. Appl. Math. 181, No. 2, 266-279 (2005). MSC: 65L05 65L06 34A34 65L20 PDFBibTeX XMLCite \textit{S. González-Pinto} and \textit{R. Rojas-Bello}, J. Comput. Appl. Math. 181, No. 2, 266--279 (2005; Zbl 1072.65100) Full Text: DOI
Amodio, Pierluigi; Sgura, Ivonne High-order finite difference schemes for the solution of second-order BVPs. (English) Zbl 1073.65061 J. Comput. Appl. Math. 176, No. 1, 59-76 (2005). Reviewer: M. Plum (Karlsruhe) MSC: 65L10 65L12 34B15 PDFBibTeX XMLCite \textit{P. Amodio} and \textit{I. Sgura}, J. Comput. Appl. Math. 176, No. 1, 59--76 (2005; Zbl 1073.65061) Full Text: DOI
Zhang, Chengjian; Vandewalle, Stefan Stability analysis of Volterra delay-integro-differential equations and their backward differentiation time discretization. (English) Zbl 1047.65117 J. Comput. Appl. Math. 164-165, 797-814 (2004). Reviewer: Stanislav Míka (Plzeň) MSC: 65R20 45M10 45J05 45G15 PDFBibTeX XMLCite \textit{C. Zhang} and \textit{S. Vandewalle}, J. Comput. Appl. Math. 164--165, 797--814 (2004; Zbl 1047.65117) Full Text: DOI
Koto, Toshiyuki Stability of Runge-Kutta methods for delay integro-differential equations. (English) Zbl 1002.65148 J. Comput. Appl. Math. 145, No. 2, 483-492 (2002). Reviewer: Nikolay Yakovlevich Tikhonenko (Odessa) MSC: 65R20 45G10 45J05 45M10 PDFBibTeX XMLCite \textit{T. Koto}, J. Comput. Appl. Math. 145, No. 2, 483--492 (2002; Zbl 1002.65148) Full Text: DOI
Fredebeul, Ch.; Kornmaier, D.; Müller, M. W. Multiple order double output Runge-Kutta Fehlberg formulae: Strategies for efficient application. (English) Zbl 1002.65076 J. Comput. Appl. Math. 144, No. 1-2, 187-196 (2002). MSC: 65L06 65L05 65L50 34A34 PDFBibTeX XMLCite \textit{Ch. Fredebeul} et al., J. Comput. Appl. Math. 144, No. 1--2, 187--196 (2002; Zbl 1002.65076) Full Text: DOI
Cash, J. R.; Garcia, M. P.; Moore, D. R. Mono-implicit Runge-Kutta formulae for the numerical solution of second order nonlinear two-point boundary value problems. (English) Zbl 1001.65079 J. Comput. Appl. Math. 143, No. 2, 275-289 (2002). MSC: 65L06 65L10 34B15 PDFBibTeX XMLCite \textit{J. R. Cash} et al., J. Comput. Appl. Math. 143, No. 2, 275--289 (2002; Zbl 1001.65079) Full Text: DOI
Baker, C. T. H.; Paul, C. A. H.; Tian, H. Differential algebraic equations with after-effect. (English) Zbl 0996.65077 J. Comput. Appl. Math. 140, No. 1-2, 63-80 (2002). MSC: 65L80 34E15 65L05 34A09 34K28 PDFBibTeX XMLCite \textit{C. T. H. Baker} et al., J. Comput. Appl. Math. 140, No. 1--2, 63--80 (2002; Zbl 0996.65077) Full Text: DOI
Baker, Christopher T. H. Retarded differential equations. (English) Zbl 0970.65079 J. Comput. Appl. Math. 125, No. 1-2, 309-335 (2000). Reviewer: R.S.Dahiya (Ames) MSC: 65L05 34K28 PDFBibTeX XMLCite \textit{C. T. H. Baker}, J. Comput. Appl. Math. 125, No. 1--2, 309--335 (2000; Zbl 0970.65079) Full Text: DOI
Paul, Christopher A. H. Designing efficient software for solving delay differential equations. (English) Zbl 0970.65078 J. Comput. Appl. Math. 125, No. 1-2, 287-295 (2000). Reviewer: R.S.Dahiya (Ames) MSC: 65L05 34K28 65L20 PDFBibTeX XMLCite \textit{C. A. H. Paul}, J. Comput. Appl. Math. 125, No. 1--2, 287--295 (2000; Zbl 0970.65078) Full Text: DOI
Enright, W. H. Continuous numerical methods for ODEs with defect control. (English) Zbl 0982.65078 J. Comput. Appl. Math. 125, No. 1-2, 159-170 (2000). Reviewer: Thomas Sonar (Braunschweig) MSC: 65L05 34A34 34B15 34A09 65L70 65L10 65L80 34K25 PDFBibTeX XMLCite \textit{W. H. Enright}, J. Comput. Appl. Math. 125, No. 1--2, 159--170 (2000; Zbl 0982.65078) Full Text: DOI
Cash, J. R. Modified extended backward differentiation formulae for the numerical solution of stiff initial value problems in ODEs and DAEs. (English) Zbl 0971.65063 J. Comput. Appl. Math. 125, No. 1-2, 117-130 (2000). Reviewer: K.T.S.R.Iyengar (Bangalore) MSC: 65L05 34A34 34A09 65L80 PDFBibTeX XMLCite \textit{J. R. Cash}, J. Comput. Appl. Math. 125, No. 1--2, 117--130 (2000; Zbl 0971.65063) Full Text: DOI
Shampine, L. F.; Corless, Robert M. Initial value problems for ODEs in problem solving environments. (English) Zbl 0971.65062 J. Comput. Appl. Math. 125, No. 1-2, 31-40 (2000). Reviewer: K.T.S.R.Iyengar (Bangalore) MSC: 65L05 34A34 68T20 68Q30 PDFBibTeX XMLCite \textit{L. F. Shampine} and \textit{R. M. Corless}, J. Comput. Appl. Math. 125, No. 1--2, 31--40 (2000; Zbl 0971.65062) Full Text: DOI
Butcher, J. C. Numerical methods for ordinary differential equations in the 20th century. (English) Zbl 0969.65063 J. Comput. Appl. Math. 125, No. 1-2, 1-29 (2000). Reviewer: Dana Petcu (Timişoara) MSC: 65L05 65L06 01A60 65-03 34A34 PDFBibTeX XMLCite \textit{J. C. Butcher}, J. Comput. Appl. Math. 125, No. 1--2, 1--29 (2000; Zbl 0969.65063) Full Text: DOI
van der Houwen, P. J.; Messina, E.; Sommeijer, B. P. Oscillatory Störmer-Cowell methods. (English) Zbl 0949.65078 J. Comput. Appl. Math. 115, No. 1-2, 547-564 (2000). Reviewer: E.Schechter (Kaiserslautern) MSC: 65L06 65L05 34A34 34C25 PDFBibTeX XMLCite \textit{P. J. van der Houwen} et al., J. Comput. Appl. Math. 115, No. 1--2, 547--564 (2000; Zbl 0949.65078) Full Text: DOI
Hairer, Ernst; Wanner, Gerhard Stiff differential equations solved by Radau methods. (English) Zbl 0945.65080 J. Comput. Appl. Math. 111, No. 1-2, 93-111 (1999). Reviewer: R.Scherer (Karlsruhe) MSC: 65L06 65L05 34A34 PDFBibTeX XMLCite \textit{E. Hairer} and \textit{G. Wanner}, J. Comput. Appl. Math. 111, No. 1--2, 93--111 (1999; Zbl 0945.65080) Full Text: DOI
Cong, Nguyen Huu Continuous variable stepsize explicit pseudo two-step RK methods. (English) Zbl 0947.65085 J. Comput. Appl. Math. 101, No. 1-2, 105-116 (1999). Reviewer: H.Brunner (St.John’s) MSC: 65L06 65L05 65L50 65L70 65Y05 PDFBibTeX XMLCite \textit{N. H. Cong}, J. Comput. Appl. Math. 101, No. 1--2, 105--116 (1999; Zbl 0947.65085) Full Text: DOI
Voss, D. A.; Muir, P. H. Mono-implicit Runge-Kutta schemes for the parallel solution of initial value ODEs. (English) Zbl 0945.65077 J. Comput. Appl. Math. 102, No. 2, 235-252 (1999). Reviewer: Iulian Coroian (Baia Mare) MSC: 65L06 65Y05 65L05 34A34 65L20 65H10 65Y20 PDFBibTeX XMLCite \textit{D. A. Voss} and \textit{P. H. Muir}, J. Comput. Appl. Math. 102, No. 2, 235--252 (1999; Zbl 0945.65077) Full Text: DOI
De Meyer, H.; Vanden Berghe, G.; Van Hecke, T.; Van Daele, M. On the generation of mono-implicit Runge-Kutta-Nyström methods by mono-implicit Runge-Kutta methods. (English) Zbl 0898.65047 J. Comput. Appl. Math. 87, No. 1, 147-167 (1997). Reviewer: H.Ade (Mainz) MSC: 65L06 65L05 34A34 65L20 PDFBibTeX XMLCite \textit{H. De Meyer} et al., J. Comput. Appl. Math. 87, No. 1, 147--167 (1997; Zbl 0898.65047) Full Text: DOI
Aïd, René; Levacher, Laurent Numerical investigations on global error estimation for ordinary differential equations. (English) Zbl 0887.65096 J. Comput. Appl. Math. 82, No. 1-2, 21-39 (1997). Reviewer: J.D.P.Donnelly (Oxford) MSC: 65L70 65L05 34A34 PDFBibTeX XMLCite \textit{R. Aïd} and \textit{L. Levacher}, J. Comput. Appl. Math. 82, No. 1--2, 21--39 (1997; Zbl 0887.65096) Full Text: DOI
Papageorgiou, G.; Tsitouras, Ch. Continuous Runge-Kutta(-Nyström) methods with reduced phase-errors. (English) Zbl 0855.65077 J. Comput. Appl. Math. 69, No. 1, 1-11 (1996). Reviewer: E.Hairer (Genève) MSC: 65L06 65L05 34C15 34A34 65L70 70K40 PDFBibTeX XMLCite \textit{G. Papageorgiou} and \textit{Ch. Tsitouras}, J. Comput. Appl. Math. 69, No. 1, 1--11 (1996; Zbl 0855.65077) Full Text: DOI
González-Pinto, S.; Montijano, J. I.; Rández, L. Improving the efficiency of the iterative schemes for implicit Runge-Kutta methods. (English) Zbl 0856.65084 J. Comput. Appl. Math. 66, No. 1-2, 227-238 (1996). Reviewer: J.D.P.Donnelly (Oxford) MSC: 65L06 65L05 34E13 34A34 PDFBibTeX XMLCite \textit{S. González-Pinto} et al., J. Comput. Appl. Math. 66, No. 1--2, 227--238 (1996; Zbl 0856.65084) Full Text: DOI
Owren, B. Stability of Runge-Kutta methods used in modular integration. (English) Zbl 0839.65087 J. Comput. Appl. Math. 62, No. 1, 89-101 (1995). Reviewer: R.Scherer (Karlsruhe) MSC: 65L20 65L06 65L05 34A30 PDFBibTeX XMLCite \textit{B. Owren}, J. Comput. Appl. Math. 62, No. 1, 89--101 (1995; Zbl 0839.65087) Full Text: DOI
Shampine, L. F.; Witt, A. A simple step size selection algorithm for ODE codes. (English) Zbl 0842.65052 J. Comput. Appl. Math. 58, No. 3, 345-354 (1995). Reviewer: J.B.Butler jun.(Portland) MSC: 65L50 65L05 34A34 PDFBibTeX XMLCite \textit{L. F. Shampine} and \textit{A. Witt}, J. Comput. Appl. Math. 58, No. 3, 345--354 (1995; Zbl 0842.65052) Full Text: DOI
Higham, Desmond J.; Famelis, Ioannis Th. Equilibrium states of adaptive algorithms for delay differential equations. (English) Zbl 0833.65070 J. Comput. Appl. Math. 58, No. 2, 151-169 (1995). Reviewer: M.Bartušek (Brno) MSC: 65L06 65L05 34K05 PDFBibTeX XMLCite \textit{D. J. Higham} and \textit{I. Th. Famelis}, J. Comput. Appl. Math. 58, No. 2, 151--169 (1995; Zbl 0833.65070) Full Text: DOI
Zhang, Wen The starting procedure in variable-stepsize variable-order PECE codes. (English) Zbl 0817.65062 J. Comput. Appl. Math. 53, No. 1, 73-86 (1994). Reviewer: N.Vulchanov (Gabrovo) MSC: 65L06 65L05 34A34 PDFBibTeX XMLCite \textit{W. Zhang}, J. Comput. Appl. Math. 53, No. 1, 73--86 (1994; Zbl 0817.65062) Full Text: DOI
Dekker, T. J.; Hoffmann, W.; Potma, K. Parallel algorithms for solving large linear systems. (English) Zbl 0808.65020 J. Comput. Appl. Math. 50, No. 1-3, 221-232 (1994). Reviewer: W.Schönauer (Karlsruhe) MSC: 65F05 65Y05 PDFBibTeX XMLCite \textit{T. J. Dekker} et al., J. Comput. Appl. Math. 50, No. 1--3, 221--232 (1994; Zbl 0808.65020) Full Text: DOI
Cong, Nguyen huu Parallel iteration of symmetric Runge-Kutta methods for nonstiff initial-value problems. (English) Zbl 0804.65070 J. Comput. Appl. Math. 51, No. 1, 117-125 (1994). Reviewer: I.N.Katz (St.Louis) MSC: 65L06 65L05 65Y05 34A34 PDFBibTeX XMLCite \textit{N. h. Cong}, J. Comput. Appl. Math. 51, No. 1, 117--125 (1994; Zbl 0804.65070) Full Text: DOI
Shampine, Lawrence F. Ill-conditioned matrices and the integration of stiff ODEs. (English) Zbl 0798.65081 J. Comput. Appl. Math. 48, No. 3, 279-292 (1993). Reviewer: M.Plum (Clausthal-Zellerfeld) MSC: 65L06 65L05 34A34 34E13 PDFBibTeX XMLCite \textit{L. F. Shampine}, J. Comput. Appl. Math. 48, No. 3, 279--292 (1993; Zbl 0798.65081) Full Text: DOI
Higham, Desmond J. The tolerance proportionality of adaptive ODE solvers. (English) Zbl 0780.65050 J. Comput. Appl. Math. 45, No. 1-2, 227-236 (1993). MSC: 65L70 65L05 65L50 65L06 34A34 PDFBibTeX XMLCite \textit{D. J. Higham}, J. Comput. Appl. Math. 45, No. 1--2, 227--236 (1993; Zbl 0780.65050) Full Text: DOI
Cooper, G. J.; Vignesvaran, R. Some schemes for the implementation of implicit Runge-Kutta methods. (English) Zbl 0783.65064 J. Comput. Appl. Math. 45, No. 1-2, 213-225 (1993). Reviewer: L.-I.Anita (Iaşi) MSC: 65L06 65F10 65L05 34A30 PDFBibTeX XMLCite \textit{G. J. Cooper} and \textit{R. Vignesvaran}, J. Comput. Appl. Math. 45, No. 1--2, 213--225 (1993; Zbl 0783.65064) Full Text: DOI
Butcher, J. C.; Johnston, P. B. Estimating local truncation errors for Runge-Kutta methods. (English) Zbl 0789.65066 J. Comput. Appl. Math. 45, No. 1-2, 203-212 (1993). Reviewer: H.Ade (Mainz) MSC: 65L70 65L06 34A34 PDFBibTeX XMLCite \textit{J. C. Butcher} and \textit{P. B. Johnston}, J. Comput. Appl. Math. 45, No. 1--2, 203--212 (1993; Zbl 0789.65066) Full Text: DOI
Vermiglio, R. Multistep high-order interpolants of Runge-Kutta methods. (English) Zbl 0780.65044 J. Comput. Appl. Math. 45, No. 1-2, 75-88 (1993). MSC: 65L06 65L05 34A34 PDFBibTeX XMLCite \textit{R. Vermiglio}, J. Comput. Appl. Math. 45, No. 1--2, 75--88 (1993; Zbl 0780.65044) Full Text: DOI
Sharp, P. W.; Fine, J. M. A contrast of direct and transformed Nyström pairs. (English) Zbl 0765.65082 J. Comput. Appl. Math. 42, No. 3, 293-308 (1992). Reviewer: E.Schechter (Kaiserslautern) MSC: 65L06 65L20 34A34 PDFBibTeX XMLCite \textit{P. W. Sharp} and \textit{J. M. Fine}, J. Comput. Appl. Math. 42, No. 3, 293--308 (1992; Zbl 0765.65082) Full Text: DOI
Sharp, P. W.; Fine, J. M. Some Nyström pairs for the general second-order initial-value problem. (English) Zbl 0765.65081 J. Comput. Appl. Math. 42, No. 3, 279-291 (1992). Reviewer: E.Schechter (Kaiserslautern) MSC: 65L06 65L05 65L70 34A34 PDFBibTeX XMLCite \textit{P. W. Sharp} and \textit{J. M. Fine}, J. Comput. Appl. Math. 42, No. 3, 279--291 (1992; Zbl 0765.65081) Full Text: DOI
Higham, D. J. Monotonic piecewise cubic interpolation, with applications to ODE plotting. (English) Zbl 0768.65002 J. Comput. Appl. Math. 39, No. 3, 287-294 (1992). Reviewer: V.A.Velev (Sofia) MSC: 65D05 65L05 PDFBibTeX XMLCite \textit{D. J. Higham}, J. Comput. Appl. Math. 39, No. 3, 287--294 (1992; Zbl 0768.65002) Full Text: DOI
Marletta, Marco; Pryce, John D. Automatic solution of Sturm-Liouville problems using the Pruess method. (English) Zbl 0747.65070 J. Comput. Appl. Math. 39, No. 1, 57-78 (1992). Reviewer: O.Titow (Berlin) MSC: 65L15 65L50 34L15 PDFBibTeX XMLCite \textit{M. Marletta} and \textit{J. D. Pryce}, J. Comput. Appl. Math. 39, No. 1, 57--78 (1992; Zbl 0747.65070) Full Text: DOI
Coleman, John P.; Booth, Andrew S. Analysis of a family of Chebyshev methods for \(y''=f(x,y)\). (English) Zbl 0773.65048 J. Comput. Appl. Math. 44, No. 1, 95-114 (1992). Reviewer: F.Ling (Hoboken) MSC: 65L06 65L05 65L20 34A34 PDFBibTeX XMLCite \textit{J. P. Coleman} and \textit{A. S. Booth}, J. Comput. Appl. Math. 44, No. 1, 95--114 (1992; Zbl 0773.65048) Full Text: DOI
Sugiura, Hiroshi; Torii, Tatsuo A method for constructing generalized Runge-Kutta methods. (English) Zbl 0747.65062 J. Comput. Appl. Math. 38, No. 1-3, 399-410 (1991). Reviewer: O.Titow (Berlin) MSC: 65L06 65L05 65L70 34A34 65H10 PDFBibTeX XMLCite \textit{H. Sugiura} and \textit{T. Torii}, J. Comput. Appl. Math. 38, No. 1--3, 399--410 (1991; Zbl 0747.65062) Full Text: DOI
Stewart, Kris A model for stability of the semi-implicit backward differentiation formulas. (English) Zbl 0725.65072 J. Comput. Appl. Math. 33, No. 3, 245-259 (1990). Reviewer: V.Prepeliţă (Bucureşti) MSC: 65L05 65L20 34E13 34A34 PDFBibTeX XMLCite \textit{K. Stewart}, J. Comput. Appl. Math. 33, No. 3, 245--259 (1990; Zbl 0725.65072) Full Text: DOI
Rios Neto, Atair; Rama Rao, Kondapalli A stochastic approach to global error estimation in ODE multistep numerical integration. (English) Zbl 0704.65061 J. Comput. Appl. Math. 30, No. 3, 257-281 (1990). Reviewer: I.Dimov MSC: 65L70 65L05 65L06 34A34 PDFBibTeX XMLCite \textit{A. Rios Neto} and \textit{K. Rama Rao}, J. Comput. Appl. Math. 30, No. 3, 257--281 (1990; Zbl 0704.65061) Full Text: DOI
Stewart, Kris Avoiding stability-induced inefficiencies in BDF methods. (English) Zbl 0699.65067 J. Comput. Appl. Math. 29, No. 3, 357-367 (1990). Reviewer: T.Mitsui MSC: 65L20 65L05 34A34 PDFBibTeX XMLCite \textit{K. Stewart}, J. Comput. Appl. Math. 29, No. 3, 357--367 (1990; Zbl 0699.65067) Full Text: DOI
Calvo, M.; Montijano, J. I.; Randez, L. A fifth-order interpolant for the Dormand and Prince Runge-Kutta method. (English) Zbl 0687.65078 J. Comput. Appl. Math. 29, No. 1, 91-100 (1990). Reviewer: A.Coţiu MSC: 65L05 34A34 PDFBibTeX XMLCite \textit{M. Calvo} et al., J. Comput. Appl. Math. 29, No. 1, 91--100 (1990; Zbl 0687.65078) Full Text: DOI
van der Houwen, P. J.; Sommeijer, B. P. Parallel iteration of high-order Runge-Kutta methods with stepsize control. (English) Zbl 0682.65039 J. Comput. Appl. Math. 29, No. 1, 111-127 (1990). Reviewer: E.Hairer MSC: 65L05 65L50 34A34 PDFBibTeX XMLCite \textit{P. J. van der Houwen} and \textit{B. P. Sommeijer}, J. Comput. Appl. Math. 29, No. 1, 111--127 (1990; Zbl 0682.65039) Full Text: DOI
van der Houwen, P. J.; Sommeijer, B. P.; van Mourik, P. A. Note on explicit parallel multistep Runge-Kutta methods. (English) Zbl 0683.65056 J. Comput. Appl. Math. 27, No. 3, 411-420 (1989). Reviewer: P.Chocholatý MSC: 65L05 65Y05 65L20 34A34 PDFBibTeX XMLCite \textit{P. J. van der Houwen} et al., J. Comput. Appl. Math. 27, No. 3, 411--420 (1989; Zbl 0683.65056) Full Text: DOI
Carroll, John A composite integration scheme for the numerical solution of systems of ordinary differential equations. (English) Zbl 0664.65072 J. Comput. Appl. Math. 25, No. 1, 1-13 (1989). Reviewer: J.M.Sanz-Serna MSC: 65L05 65L20 34A34 PDFBibTeX XMLCite \textit{J. Carroll}, J. Comput. Appl. Math. 25, No. 1, 1--13 (1989; Zbl 0664.65072) Full Text: DOI
de Oliveira, Paula Some simple characterizations of contractivity regions. (English) Zbl 0661.65074 J. Comput. Appl. Math. 25, No. 1, 27-32 (1989). Reviewer: M.Bartušek MSC: 65L05 34A34 PDFBibTeX XMLCite \textit{P. de Oliveira}, J. Comput. Appl. Math. 25, No. 1, 27--32 (1989; Zbl 0661.65074) Full Text: DOI
Rockswold, Gary K. Implementation of \(\alpha\)-type multistep methods for stiff differential equations. (English) Zbl 0643.65038 J. Comput. Appl. Math. 22, No. 1, 63-69 (1988). Reviewer: M.Bartušek MSC: 65L05 65L20 34A34 34-04 PDFBibTeX XMLCite \textit{G. K. Rockswold}, J. Comput. Appl. Math. 22, No. 1, 63--69 (1988; Zbl 0643.65038) Full Text: DOI
Brankin, R. W.; Gladwell, I.; Shampine, L. F. Starting BDF and Adams codes at optimal order. (English) Zbl 0642.65056 J. Comput. Appl. Math. 21, No. 3, 357-368 (1988). Reviewer: R.Scherer MSC: 65L05 34A34 PDFBibTeX XMLCite \textit{R. W. Brankin} et al., J. Comput. Appl. Math. 21, No. 3, 357--368 (1988; Zbl 0642.65056) Full Text: DOI
Gladwell, I.; Shampine, L. F.; Brankin, R. W. Automatic selection of the initial step size for an ODE solver. (English) Zbl 0623.65080 J. Comput. Appl. Math. 18, 175-192 (1987). Reviewer: G.Hall MSC: 65L05 65L50 34A34 PDFBibTeX XMLCite \textit{I. Gladwell} et al., J. Comput. Appl. Math. 18, 175--192 (1987; Zbl 0623.65080) Full Text: DOI
Ypma, T. J. Relaxed Newton-like methods for stiff differential systems. (English) Zbl 0621.65073 J. Comput. Appl. Math. 16, 95-103 (1986). Reviewer: A.Coţiu MSC: 65L05 34A34 PDFBibTeX XMLCite \textit{T. J. Ypma}, J. Comput. Appl. Math. 16, 95--103 (1986; Zbl 0621.65073) Full Text: DOI
Dormand, J. R.; Prince, P. J. A reconsideration of some embedded Runge-Kutta formulae. (English) Zbl 0602.65046 J. Comput. Appl. Math. 15, 203-211 (1986). Reviewer: E.Schechter MSC: 65L05 65L20 34A34 PDFBibTeX XMLCite \textit{J. R. Dormand} and \textit{P. J. Prince}, J. Comput. Appl. Math. 15, 203--211 (1986; Zbl 0602.65046) Full Text: DOI