Finite Difference Computing with PDEs
by Hans Petter Langtangen, Svein Linge
Publisher: Springer 2017
Number of pages: 507
This easy-to-read book introduces the basics of solving partial differential equations by means of finite difference methods. Unlike many of the traditional academic works on the topic, this book was written for practitioners.
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by Jeffrey R. Chasnov - The Hong Kong University
This is primarily for non-mathematics majors and is required by several engineering departments. Contents: IEEE Arithmetic; Root Finding; Systems of equations; Least-squares approximation; Interpolation; Integration; Ordinary differential equations.
by Steven E. Pav - University of California at San Diego
From the table of contents: A 'Crash' Course in octave/Matlab; Solving Linear Systems; Finding Roots; Interpolation; Spline Interpolation; Approximating Derivatives; Integrals and Quadrature; Least Squares; Ordinary Differential Equations.
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This book focuses on a small number of methods and treats them in depth. The author provides a complete analysis of the conjugate gradient and generalized minimum residual iterations as well as recent advances including Newton-Krylov methods.
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These lectures introduce the modern theory and practical numerical methods for continuation of solutions of nonlinear problems depending upon parameters. The treatment is elementary, advanced calculus and linear algebra are the omly prerequisites.