Fourth order numerical method for the solution of heat equation with nonlocal boundary condition
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Date
2017-12-15
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UMT Lahore
Abstract
In this thesis, a numerical technique is developed for solving one-dimensional parabolic partial differential equation (PDE) with integral boundary conditions. The spatial derivative is approximated by a finite difference (FD) scheme, and by applying the method of lines, resulting in a system of ordinary differential equations (ODEs). Simpson’s 1/3 rule is used to tackle integral boundary conditions, and it also helps in removing additional variables to produce a system of N equations with N variables. This numerical method can be coded in sequential as well as parallel computing environments.