Muhammad Aziz Ur RehmanM. S. A. TajMuhammad SaeedI. Rehman2012-11-082012-11-082012Archives Des Sciences Vol 65, No. 4; Apr 2012, 119-1301661-464Xhttps://escholar.umt.edu.pk/handle/123456789/637A 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 .enMathematicsMethod of LinesNon-Local Boundary ConditionArticle