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.

References in zbMATH (referenced in 49 articles , 2 standard articles )

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  1. Ditkowski, Adi; Gottlieb, Sigal; Grant, Zachary J.: Explicit and implicit error inhibiting schemes with post-processing (2020)
  2. Hoang, H. S.; Baraille, Remy: A simple numerical method based simultaneous stochastic perturbation for estimation of high dimensional matrices (2019)
  3. Fukui, Tomohiro; Kawaguchi, Misa; Morinishi, Koji: A two-way coupling scheme to model the effects of particle rotation on the rheological properties of a semidilute suspension (2018)
  4. Sewell, Granville: Solving partial differential equation applications with PDE2D (2018)
  5. Ditkowski, A.; Gottlieb, S.: Error inhibiting block one-step schemes for ordinary differential equations (2017)
  6. Abdoulkary, Saidou; English, L. Q.; Mohamadou, Alidou: Envelope solitons in a left-handed nonlinear transmission line with Josephson junction (2016)
  7. Dang, Duy-Minh; Nguyen, Duy; Sewell, Granville: Numerical schemes for pricing Asian options under state-dependent regime-switching jump-diffusion models (2016)
  8. Camacho, Carmen; Pérez-Barahona, Agustín: Land use dynamics and the environment (2015)
  9. Mariani, Maria C.; Sengupta, Indranil; Sewell, Granville: Numerical methods applied to option pricing models with transaction costs and stochastic volatility (2015)
  10. Sewell, Granville: The numerical solution of ordinary and partial differential equations. (2015)
  11. Florescu, Ionuţ; Mariani, Maria Cristina; Sewell, Granville: Numerical solutions to an integro-differential parabolic problem arising in the pricing of financial options in a Levy market (2014)
  12. Lanzafame, G.: Implicit integrations for SPH in semi-Lagrangian approach: application to the accretion disc modeling in a microquasar (2013)
  13. Sewell, Granville: (Free) software for general partial differential equation problems in non-rectangular 2D and 3D regions (2013)
  14. Sewell, Granville: Solving the KPI wave equation with a moving adaptive FEM grid (2013)
  15. Cui, Mingrong: Compact alternating direction implicit method for two-dimensional time fractional diffusion equation (2012)
  16. Arregui, I.; Soler, R.; Ballester, J. L.; Wright, A. N.: Magnetohydrodynamic kink waves in two-dimensional non-uniform prominence threads (2011)
  17. Lalegname, A.; Sändig, A.-M.: Wave-crack interaction in finite elastic bodies (2011)
  18. Lang, Moritz; Marquez-Lago, Tatiana T.; Stelling, Jörg; Waldherr, Steffen: Autonomous synchronization of chemically coupled synthetic oscillators (2011)
  19. Acosta, Sebastian; Villamizar, Vianey: Finite difference on grids with nearly uniform cell area and line spacing for the wave equation on complex domains (2010)
  20. Cui, Mingrong: High order compact alternating direction implicit method for the generalized sine-Gordon equation (2010)

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