M. A. REHMANM. S. A. TAJS. A. MARDAN2015-03-052015-03-05201430. Rehman, M., Taj, M., & Mardan, S. (2014). Fifth order numerical method for heat equation with nonlocal boundary conditions. Journal of Mathematical and Computational Science, 4(6), 1044-1054.https://escholar.umt.edu.pk/handle/123456789/1432This 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.enheat equationnonlocal boundary conditionfifth-order numerical methodsmethod of linesparallel algorithmArticle