Abstract:
This paper deals with numerical method for the approximate solution of one-dimensional heat equation du/dt =d2u/dx2=q(x,t) 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.
Page(s):
1-6
DOI:
DOI not available
Published:
Journal: Science International, Volume: 24, Issue: 1, Year: 2012