## PDE2D

 swMATH ID: 4270 Software Authors: Fitzgerald, Rosa M.; Sewell, Granville Description: The numerical solution of ordinary and partial differential equations. The Second Edition of this popular text provides an insightful introduction to the use of finite difference and finite element methods for the computational solution of ordinary and partial differential equations. Readers gain a thorough understanding of the theory underlying themethods presented in the text. The author emphasizes the practical steps involved in implementing the methods, culminating in readers learning how to write programs using FORTRAN90 and MATLAB(r) to solve ordinary and partial differential equations.par The book begins with a review of direct methods for the solution of linear systems, with an emphasis on the special features of the linear systems that arise when differential equations are solved. The following four chapters introduce and analyze the more commonly used finite difference methods for solving a variety of problems, including ordinary and partial differential equations and initial value and boundary value problems. The techniques presented in these chapters, with the aid of carefully developed exercises and numerical examples, can be easilymastered by readers.par The final chapter of the text presents the basic theory underlying the finite element method. Following the guidance offered in this chapter, readers gain a solid understanding of the method and discover how to use it to solve many problems.par A special feature of the Second Edition is Appendix A, which describes a finite element program, PDE2D, developed by the author. Readers discover how PDE2D can be used to solve difficult partial differential equation problems, including nonlinear time-dependent and steady-state systems, and linear eigenvalue systems in 1D intervals, general 2D regions, and a wide range of simple 3D regions. The software itself is available to instructors who adopt the text to share with their students. Homepage: http://www.pde2d.com Keywords: differential equations; numerical solution; finite differences; finite elements; initial value problems; boundary value problems; textbook; convergence; algorithms; FORTRAN 90 programs; explicit and implicit one-step and multistep methods; line methods; hyperbolic transport and wave equations; package PDE2D Related Software: ODEPACK; Matlab; nag; NAG; GitHub; EnKF; WAVEGIDE; IMSL Numerical Libraries; EISPACK; gnuplot; ma2dfc; MUMPS; TWODEPEP; KELLEY; AutoMOTGen; HSolver; RSOLVER; SMV; PHAVer; HySAT Cited in: 49 Publications
all top 5

### Cited by 72 Authors

 11 Sewell, Granville 3 Arregui, Iñigo A. 3 Ballester, J. L. 3 Baraille, Rémy 3 Cui, Mingrong 3 Lalegname, Adriana E. 2 Acosta, Sebastian 2 Camacho, Carmen 2 Ditkowski, Adi 2 Gottlieb, Sigal 2 Hoang, S. 2 Mariani, Maria Cristina 2 Sändig, Anna-Margarete 2 Talagrand, Olivier 2 Terradas, J. 2 Villamizar, Vianey 1 Abdoulkary, Saïdou 1 Andries, Johan 1 Basebi, T. 1 Bellomo, Nicola 1 Bischof, Christian H. 1 Briani, Maya 1 Chakrabarty, Siddhartha P. 1 Dang, Duy Minh 1 Das, Bigyani 1 de Mey, P. 1 Dilão, Rui 1 Doman, David B. 1 Dorn, Oliver 1 Eberhard, Peter 1 English, Lars Q. 1 Fitzgerald, Rosa M. 1 Florescu, Ionuţ 1 Fukui, Tomohiro 1 Goossens, Marcel 1 Grant, Zachary J. 1 Hanson, Floyd B. 1 Hoang, Hong Son 1 Holsapple, Raymond W. 1 Iyer, Ram Venkataraman 1 Jorquera, Héctor 1 Karttunen, Mikko 1 Kawaguchi, Misa 1 Koch, Manfred 1 Lang, Annika 1 Lang, Moritz 1 Lanzafame, G. 1 Leippold, Markus 1 Marquez-Lago, Tatiana T. 1 Mohamadou, Alidou 1 Morinishi, Koji 1 Oliver, Ramón 1 Patra, Michael 1 Pérez-Barahona, Agustín 1 Preziosi, Luigi 1 Ratschan, Stefan 1 Robey, Thomas H. 1 Ruderman, Michael S. 1 Sainhas, Joaquim 1 SenGupta, Indranil 1 Smaus, Jan-Georg 1 Soler, Roger 1 Steinberg, Stanly L. 1 Stelling, Jörg 1 Valls, Oriol T. 1 van Doorsselaere, T. 1 Waldherr, Steffen 1 Wright, A. N. 1 Wu, Liuren 1 Zhang, Danjie 1 Zou, Benteng 1 Žutić, Igor
all top 5

### Cited in 25 Serials

 4 Astronomy and Astrophysics 3 Computer Physics Communications 3 Journal of Computational and Applied Mathematics 2 Computers and Fluids 2 Computers & Mathematics with Applications 2 Journal of Computational Physics 2 Kybernetika 2 Mathematics and Computers in Simulation 2 Numerical Methods for Partial Differential Equations 2 Quantitative Finance 2 International Journal of Fracture 2 Bulletin of Computational Applied Mathematics 1 Mathematical Biosciences 1 Mathematics of Computation 1 Bulletin of Mathematical Biology 1 Chaos, Solitons and Fractals 1 Journal of Economic Dynamics & Control 1 Journal of Scientific Computing 1 Multidimensional Systems and Signal Processing 1 European Journal of Operational Research 1 International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 1 Advances in Engineering Software 1 European Finance Review 1 International Journal of Numerical Analysis and Modeling 1 Pure and Applied Mathematics. A Wiley-Interscience Series of Texts, Monographs and Tracts
all top 5

### Cited in 20 Fields

 32 Numerical analysis (65-XX) 14 Partial differential equations (35-XX) 7 Ordinary differential equations (34-XX) 6 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 5 Fluid mechanics (76-XX) 5 Astronomy and astrophysics (85-XX) 3 Biology and other natural sciences (92-XX) 3 Systems theory; control (93-XX) 2 Integral equations (45-XX) 2 Calculus of variations and optimal control; optimization (49-XX) 2 Probability theory and stochastic processes (60-XX) 2 Computer science (68-XX) 2 Mechanics of deformable solids (74-XX) 2 Statistical mechanics, structure of matter (82-XX) 1 General and overarching topics; collections (00-XX) 1 Difference and functional equations (39-XX) 1 Mechanics of particles and systems (70-XX) 1 Optics, electromagnetic theory (78-XX) 1 Classical thermodynamics, heat transfer (80-XX) 1 Quantum theory (81-XX)