Browsing by Author "M. S. A. Taj"

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    Fourth-order method for the solution of diffusion equation subject to the specification of energy
    (Society of Physics and Natural History of Geneva, 2012) Muhammad Aziz Ur Rehman; M. S. A. Taj; Muhammad Saeed; I. Rehman
    A fourth-order numerical technique is developed for the solution of the diffusion equation ( ut =uxx + s x, t),0 < x < X,0 < t £ T, subject to u(x,0) = f (x),0 < x < X,u(1, t) = g(t),0 < t £ T and the specification of energy 0 ( , ) ( ), 0 , 0 b u x t dx = M t < b < X < t £ T .
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    A numerical technique for heat equation subject to integral specifications
    (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.