Efficient numerical technique for homogeneous heat equation subject to a boundary integral specification

This paper deals with numerical method for the approximate solution of one-dimension heat equation with integral condition. The integral condition is approximated by using Simpson's 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 a problem and found to be highly accurate when compared with the exact ones and the alternative techniques.