(Science International, 2011) Muhammad Aziz Ur Rehman; M. S. A. Taj
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.