A numerical technique for heat equation subject to integral specifications
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Date
2011
Authors
Journal Title
Journal ISSN
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Publisher
Science International
Abstract
This paper deals with numerical method for the approximate solution of one-dimensional
heat equation with integral boundary conditions. The integral conditions are
approximated by using Simpson’s 1/3 rule while the space derivatives are approximated by third-order
finite difference approximations. Then method of lines, semidiscritization approach, is used to transform
the model partial differential equation into a system of first-order linear ordinary differential equations
whose solution satisfies a recurrence relation involving matrix exponential function. The method developed
is L-acceptable, third-order accurate in space and time and do not require the use of complex arithmetic. A
parallel algorithm is also developed and implemented on several problems from literature and found to be
highly accurate when compared with the exact ones and alternative techniques.
Description
Keywords
Mathematics, Parallel Algorithm, Third Order Numerical Methods, Method of Lines, Boundary Integral Specifications
Citation
Sci.Int.(Lahore), 24(1), 1-6, 2011