Muhammad Aziz Ur RehmanS. A MardanM. S. A TajA Bhatti. A.2012-05-172012-05-172012International Mathematical Forum 7(32), 1567-1580, 2012https://escholar.umt.edu.pk/handle/123456789/496A 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.enHeat Equation,Fifth Order Numerical MethodsHigher Order Pde’s ApproximationsMethod of LinesParallel AlgorithmArticle