Abstract
This chapter describes methods for solving boundary value problems. One-dimensional problems are solved using the shooting method. A description of the finite difference approximation method is provided, and the method is applied to one-dimensional boundary value problems and to parabolic, hyperbolic, and elliptic partial differential equations in two dimensions. The finite difference approximation approach is implemented in Matlab and used to solve the one-dimensional heat-flow equation (parabolic equation), the wave equation (hyperbolic equation), and the Laplace, Helmholtz, and Poisson equations (elliptic equations). Problems and solutions are provided.
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