Browsing by Author "M. A. REHMAN"

Now showing 1 - 1 of 1
  • Thumbnail Image
    Item
    Fifth order numerical method for heat equation with nonlocal boundary conditions
    (Journal of Mathematical and Computational Science, 2014) M. A. REHMAN; M. S. A. TAJ; S. A. MARDAN
    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.