Muhammad Aziz Ur RehmanM. S. A. Taj2012-11-082012-11-082011Sci.Int.(Lahore), 24(1), 1-6, 20111013-5316https://escholar.umt.edu.pk/handle/123456789/636This 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.enMathematicsParallel AlgorithmThird Order Numerical MethodsMethod of LinesBoundary Integral SpecificationsArticle