The Numerical Approximation of Functional Differential Equations
by Daniele Venturi
Publisher: arXiv 2016
Number of pages: 113
The purpose of this manuscript is to provide a new perspective on the problem of numerical approximation of nonlinear functionals and functional differential equations. The proposed methods will be described and demonstrated in various examples.
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by B. Piette - University of Durham
In these notes, we describe the design of a small C++ program which solves numerically the sine-Gordon equation. The program is build progressively to make it multipurpose and easy to modify to solve any system of partial differential equations.
by Douglas W. Harder, Richard Khoury - University of Waterloo
Contents: Error Analysis, Numeric Representation, Iteration, Linear Algebra, Interpolation, Least Squares, Taylor Series, Bracketing, The Five Techniques, Root Finding, Optimization, Differentiation, Integration, Initial-value Problems, etc.
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.
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This book presents Python programming as a key method for solving mathematical problems. The style is accessible and concise, the emphasis is on generic algorithms, clean design of programs, use of functions, and automatic tests for verification.