Fifth order numerical method for heat equation with nonlocal boundary conditions
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Date
2014
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Journal ISSN
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Publisher
Journal of Mathematical and Computational Science
Abstract
This paper deals with numerical method for the approximate solution of one dimensional heat equation ut = uxx +q(x; t) with integral boundary conditions. The integral conditions are approximated by Simpson’s 13 rule while the space derivatives are approximated by fifth-order difference approximations. The method of lines, semi discretization 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, fifth-order accurate in space and time and do not required the use of complex arithmetic. A parallel algorithm is also developed and implemented on several problems from literature and found highly accurate when compared with the exact ones and alternative techniques.
Description
Keywords
heat equation, nonlocal boundary condition, fifth-order numerical methods, method of lines, parallel algorithm
Citation
30. Rehman, M., Taj, M., & Mardan, S. (2014). Fifth order numerical method for heat equation with nonlocal boundary conditions. Journal of Mathematical and Computational Science, 4(6), 1044-1054.