Department of Mathematics

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Fusion higher -order parallel splitting methods for parabolic partial differential equations
(2012) Muhammad Aziz Ur Rehman; S. A Mardan; M. S. A Taj; A Bhatti. A.
A family of numerical methods, based upon a rational approximation to the matrix exponential function, was developed for solving parabolic partial differential equations. These methods were partially sixth-order precise in space and time, due to combination of sixth-order finite approximations and fifth-order pde’s approximations. These methods do not involve the use of complex computation. In these methods second-order spatial derivates were approximated by sixth-order finite difference approximations. Parallel algorithms were developed and tested on the one, two and three-dimensional heat equations, with constant coefficients, subject to homogeneous boundary conditions and time dependent boundary conditions. It was observed that the results obtained through these methods were highly accurate and can be easily coded on serial or parallel computers.