Bialecki, Bernard; Fernandes, Ryan I. Convergence analysis of ADI orthogonal spline collocation without perturbation terms. (English) Zbl 1499.65554 Int. J. Numer. Anal. Model. 18, No. 5, 620-641 (2021). MSC: 65M70 65M06 65N35 65M12 65D07 35K05 × Cite Format Result Cite Review PDF Full Text: Link
Fisher, Nick; Bialecki, Bernard Extrapolated ADI Crank-Nicolson orthogonal spline collocation for coupled Burgers’ equations. (English) Zbl 1433.65185 J. Difference Equ. Appl. 26, No. 1, 45-73 (2020). MSC: 65M70 65M15 35Q53 × Cite Format Result Cite Review PDF Full Text: DOI
Bialecki, B.; Dryja, M.; Fernandes, R. I. Convergence analysis of the finite difference ADI scheme for variable coefficient parabolic problems with nonzero Dirichlet boundary conditions. (English) Zbl 1420.65085 Comput. Math. Math. Phys. 58, No. 12, 2086-2108 (2018). Reviewer: Kanakadurga Sivakumar (Chennai) MSC: 65M06 65M12 35K10 × Cite Format Result Cite Review PDF Full Text: DOI
Bialecki, Bernard; Fisher, Nick Maximum norm convergence analysis of extrapolated Crank-Nicolson orthogonal spline collocation for Burgers’ equation in one space variable. (English) Zbl 1405.65131 J. Difference Equ. Appl. 24, No. 10, 1621-1642 (2018). MSC: 65M70 65M12 35Q53 65M15 65D07 65M06 × Cite Format Result Cite Review PDF Full Text: DOI
Dehghan, Mehdi The one-dimensional heat equation subject to a boundary integral specification. (English) Zbl 1139.35352 Chaos Solitons Fractals 32, No. 2, 661-675 (2007). MSC: 35K05 65M06 35K20 45K05 × Cite Format Result Cite Review PDF Full Text: DOI
Lin, Ping; Liu, Chun; Zhang, Hui An energy law preserving \(C^0\) finite element scheme for simulating the kinematic effects in liquid crystal dynamics. (English) Zbl 1133.65077 J. Comput. Phys. 227, No. 2, 1411-1427 (2007). Reviewer: Oleg A. Sinkevich (Moskva) MSC: 65M60 76A15 82D25 82-08 76A05 × Cite Format Result Cite Review PDF Full Text: DOI
Dehghan, Mehdi Efficient techniques for the second-order parabolic equation subject to nonlocal specifications. (English) Zbl 1063.65079 Appl. Numer. Math. 52, No. 1, 39-62 (2005). MSC: 65M06 35K05 65M70 65M60 × Cite Format Result Cite Review PDF Full Text: DOI
Thomée, Vidar From finite differences to finite elements. A short history of numerical analysis of partial differential equations. (English) Zbl 0977.65001 J. Comput. Appl. Math. 128, No. 1-2, 1-54 (2001). Reviewer: Gerald W.Hedstrom (Pleasanton) MSC: 65-03 01A60 65N06 65N12 35J25 65N15 65N30 65N35 65N38 × Cite Format Result Cite Review PDF Full Text: DOI
Cheng, Aijie Improvement on stability and convergence of ADI schemes. (English) Zbl 0931.65095 Appl. Math. Mech., Engl. Ed. 20, No. 1, 76-83 (1999). Reviewer: L.G.Vulkov (Russe) MSC: 65M12 35K55 65H10 65M06 65M15 × Cite Format Result Cite Review PDF Full Text: DOI
Shaw, S.; Warby, M. K.; Whiteman, J. R.; Dawnson, C.; Wheeler, M. F. Numerical techniques for the treatment of quasistatic viscoelastic stress problems in linear isotropic solids. (English) Zbl 0849.73073 Comput. Methods Appl. Mech. Eng. 118, No. 3-4, 211-237 (1994). MSC: 74S05 74S20 74D99 × Cite Format Result Cite Review PDF Full Text: DOI
Chryssoverghi, I.; Bacopoulos, A. Approximation of relaxed nonlinear parabolic optimal control problems. (English) Zbl 0796.49002 J. Optimization Theory Appl. 77, No. 1, 31-50 (1993). MSC: 49J15 49K15 × Cite Format Result Cite Review PDF Full Text: DOI
Bialecki, Bernard; Fernandes, Ryan I. Orthogonal spline collocation Laplace-modified and alternating-direction methods for parabolic problems on rectangles. (English) Zbl 0779.65063 Math. Comput. 60, No. 202, 545-573 (1993). Reviewer: S.Jiang (Bonn) MSC: 65M70 65M60 65M12 35K15 × Cite Format Result Cite Review PDF Full Text: DOI
Ames, W. F.; Postell, F. V.; Adams, E. Optimal numerical algorithms. (English) Zbl 0758.65059 Appl. Numer. Math. 10, No. 3-4, 235-259 (1992). Reviewer: V.Subba Rao (Madras) MSC: 65M06 65M12 35K50 35L70 × Cite Format Result Cite Review PDF Full Text: DOI
Jiang, Song An uncoupled numerical scheme for the equations of nonlinear one- dimensional thermoelasticity. (English) Zbl 0725.73014 J. Comput. Appl. Math. 34, No. 2, 135-144 (1991). Reviewer: J.L.Nowinski (Newark/Delaware) MSC: 74A15 74S05 74S20 74B20 65N15 × Cite Format Result Cite Review PDF Full Text: DOI
Jiang, S. Numerical solution for the Cauchy problem in nonlinear 1-D- thermoelasticity. (English) Zbl 0701.73001 Computing 44, No. 2, 147-158 (1990). Reviewer: J.Ignaczak MSC: 74A15 74B20 65M30 74S20 74S05 × Cite Format Result Cite Review PDF Full Text: DOI
Jiang, Song A \(C^ 1\) finite element collocation method for the equations of one- dimensional nonlinear thermoviscoelasticity. (English) Zbl 0675.73077 Math. Comput. Simul. 31, No. 3, 227-239 (1989). Reviewer: S.K.Lakshmana Rao MSC: 74A15 74F05 74S05 74B20 × Cite Format Result Cite Review PDF Full Text: DOI
Jiang, S. On a finite element method for the equations of one-dimensional nonlinear thermoviscoelasticity. (English) Zbl 0644.73014 Computing 40, No. 2, 111-124 (1988). Reviewer: S.Jiang MSC: 74F05 65N30 65N15 74D99 74S99 × Cite Format Result Cite Review PDF Full Text: DOI
Čermák, Libor; Zlámal, Miloš Finite element solution of a nonlinear diffusion problem with a moving boundary. (English) Zbl 0605.65078 RAIRO, Modélisation Math. Anal. Numér. 20, 403-426 (1986). MSC: 65N30 65N15 35R35 35K60 78A55 × Cite Format Result Cite Review PDF Full Text: DOI EuDML
Chou, S.-I.; Wang, C.-C. Estimates of error in finite element approximate solutions to problems in linear thermoelasticity. II. Computationally uncoupled numerical schemes. (English) Zbl 0555.73075 Arch. Ration. Mech. Anal. 85, 27-40 (1984). Reviewer: P.Narain MSC: 74S05 74F05 74S99 74A15 × Cite Format Result Cite Review PDF Full Text: DOI
Chou, S.-I.; Wang, C.-C. Estimates of error in finite element approximate solutions to problems in linear thermoelasticity. I: Computationally coupled numerical schemes. (English) Zbl 0494.73071 Arch. Ration. Mech. Anal. 77, 263-299 (1981). MSC: 74S05 74F05 65M15 × Cite Format Result Cite Review PDF Full Text: DOI
Chou, S.-I.; Wang, C.-C. Error estimates of finite element approximations for problems in linear elasticity. III: Problems in elastodynamics; discrete time approximations. (English) Zbl 0447.73063 Arch. Ration. Mech. Anal. 73, 159-182 (1980). MSC: 74S05 65M15 74B99 × Cite Format Result Cite Review PDF Full Text: DOI
Nedoma, Josef The finite element solution of parabolic equations. (English) Zbl 0427.65075 Apl. Mat. 23, 408-438 (1978). MSC: 65N30 35K60 65N15 × Cite Format Result Cite Review PDF Full Text: DOI EuDML
Wellford, L. Carter jun.; Hamdan, S. M. An analysis of an implicit finite element algorithm for geometrically nonlinear problems of structural dynamics. II: Accuracy. (English) Zbl 0383.73069 Computer Methods Appl. Mech. Engin. 14, 391-399 (1978). MSC: 74S05 74H45 74K99 35B35 35L65 65N30 × Cite Format Result Cite Review PDF Full Text: DOI
Wellford, L. Carter jun.; Hamdan, S. M. An analysis of an implicit finite element algorithm for geometrically nonlinear problems of structural dynamics. I: Stability. (English) Zbl 0383.73068 Computer Methods Appl. Mech. Engin. 14, 377-390 (1978). MSC: 74S05 74H45 74K99 35B35 35L65 65N30 × Cite Format Result Cite Review PDF Full Text: DOI
Zlamal, Milos Finite element methods for nonlinear parabolic equations. (English) Zbl 0385.65049 RAIRO, Anal. Numér. 11, 93-107 (1977). MSC: 65N30 35K55 35K60 65N12 65M12 × Cite Format Result Cite Review PDF Full Text: DOI EuDML
Ford, William H. Galerkin approximations to nonlinear pseudo-parabolic partial differential equations. (English) Zbl 0343.65047 Aequationes Math. 14, 271-291 (1976). MSC: 65N30 35K20 35S15 × Cite Format Result Cite Review PDF Full Text: DOI EuDML
Wellford, L. C. jun.; Oden, J. T. A theory of discontinuous finite element Galerkin approximations of shock waves in nonlinear elastic solids. II: Accuracy and convergence. (English) Zbl 0341.73043 Computer Methods appl. Mech. Engin. 8, 17-36 (1976). MSC: 74S05 74M20 65N30 × Cite Format Result Cite Review PDF Full Text: DOI
Zehfuß, H. Ein Differenzenverfahren für die Rayleigh-Grenzschicht. (German) Zbl 0175.52102 Ing.-Arch. 38, 15-24 (1969). × Cite Format Result Cite Review PDF Full Text: DOI
Gourlay, A. R.; Mitchell, A. R. High accuracy A.D.I. methods for parabolic equations with variable coefficients. (English) Zbl 0167.16001 Numer. Math. 12, 180-185 (1968). × Cite Format Result Cite Review PDF Full Text: DOI EuDML
Fairweather, G.; Gourlay, A. R. Some stable difference approximations to a fourth-order parabolic partial differential equation. (English) Zbl 0147.13801 Math. Comput. 21, 1-11 (1967). × Cite Format Result Cite Review PDF Full Text: DOI
Douglas, Jim jun.; Gunn, J. E. A general formulation of alternating direction methods. I: Parabolic and hyperbolic problems. (English) Zbl 0141.33103 Numer. Math. 6, 428-453 (1964). × Cite Format Result Cite Review PDF Full Text: DOI EuDML
Rose, Milton E. Finite difference schemes for differential equations. (English) Zbl 0122.12301 Math. Comput. 18, 179-195 (1964). × Cite Format Result Cite Review PDF Full Text: DOI
Lees, Milton A note on the convergence of alternating direction methods. (English) Zbl 0233.65055 Math. Comput. 16, 70-75 (1962). MSC: 65N06 65N12 35J05 × Cite Format Result Cite Review PDF Full Text: DOI
Lees, Milton Alternating direction and semi-explicit difference methods for parabolic partial differential equations. (English) Zbl 0101.34101 Numer. Math. 3, 398-412 (1961). × Cite Format Result Cite Review PDF Full Text: DOI EuDML Link