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Numerical Solution of Boundary Value Problems for Ordinary Differential Equations Robert D. Russell, Robert M. M. Mattheij, Uri M. Ascher
Publisher: Society for Industrial Mathematics

Initial and boundary value problems for second order partial differential equations. Boundary Value Problems: finite-difference method. This text provides an introduction to the numerical solution of initial and boundary value problems in ordinary differential equations on a firm theoretical basis. Existence, uniqueness, stability, convergence. Runge-Kutta of order Multistep methods: Adams-Bashforth method. Solution of linear difference equations with constant co-efficients: Numerical solution of boundary value problems, methods of finite differences, finite differences methods for solving Laplace's equation in a rectangular region, finite differences methods for solving the wave equation and heat equation. Chapter 9: Ordinary Differential Equations. Both boundary and initial value problems that returns a joint Gaussian process posterior over the solution. Initial and boundary value problems for ordinary differential equations. Elliptic, parabolic and hyperbolic partial differential equations. Numerical solution of ordinary differential equations: Taylor series method, Euler's method, modified Euler's method, Runge-Kutta formulae 4th order formula,. Existence and Uniqueness of solutions of initial value problems for first order ordinary differential equations, singular solutions of first order ODEs, system of first order ODEs. Numerical solution of partial differential equations has important applications in many application areas. This course is designed to prepare students to solve mathematical models represented by initial or boundary value problems involving partial differential equations that cannot be solved directly using standard mathematical techniques but are amenable to a computational approach. Chapter 10: Partial Differential Equations.