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. Lang, Annika: A Lax equivalence theorem for stochastic differential equations (2010)
  2. Sewell, Granville: Solving PDEs in non-rectangular 3D regions using a collocation finite element method (2010)
  3. Chakrabarty, Siddhartha P.; Hanson, Floyd B.: Distributed parameters deterministic model for treatment of brain tumors using Galerkin finite element method (2009)
  4. Cui, Mingrong: Fourth-order compact scheme for the one-dimensional sine-Gordon equation (2009)
  5. Dorn, Oliver: Shape reconstruction for an inverse radiative transfer problem arising in medical imaging (2009)
  6. Goossens, M.; Terradas, J.; Andries, J.; Arregui, I.; Ballester, J. L.: On the nature of kink MHD waves in magnetic flux tubes (2009)
  7. Lalegname, Adriana E.: Modeling, analysis and simulation of 2D dynamic crack propagation. (2009)
  8. Ratschan, Stefan; Smaus, Jan-Georg: Finding errors of hybrid systems by optimising an abstraction-based quality estimate (2009)
  9. Villamizar, Vianey; Acosta, Sebastian: Generation of smooth grids with line control for scattering from multiple obstacles (2009)
  10. Camacho, Carmen; Zou, Benteng; Briani, Maya: On the dynamics of capital accumulation across space (2008)
  11. Lalegname, A.; Sändig, A.-M.; Sewell, G.: Analytical and numerical treatment of a dynamic crack model (2008)
  12. Van Doorsselaere, T.; Ruderman, M. S.; Robertson, D.: Transverse oscillations of two parallel coronal loops (2008)
  13. Arregui, I.; Terradas, J.; Oliver, R.; Ballester, J. L.: The influence of the internal structuring of coronal loops on the properties of their damped transverse oscillations (2007)
  14. Holsapple, Raymond; Iyer, Ram; Doman, David: Variable step-size selection methods for implicit integration schemes for ODEs (2007)
  15. Patra, Michael; Karttunen, Mikko: Stencils with isotropic discretization error for differential operators (2006)
  16. Sewell, Granville: The numerical solution of ordinary and partial differential equations. (2005)
  17. Basebi, T.; Thomas, R. M.: A study of moving mesh methods applied to a thin flame propagating in a detonator delay element (2003)
  18. Leippold, Markus; Wu, Liuren: Design and estimation of quadratic term structure models (2003)
  19. Fitzgerald, Rosa M.; Sewell, Granville: Solving problems in computational physics using a general-purpose PDE solver (2000)
  20. Eberhard, Peter; Bischof, Christian: Automatic differentiation of numerical integration algorithms (1999)