Commenced in January 2007
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1 A Comparison of Some Splines-Based Methods for the One-dimensional Heat Equation

Authors: Ahmad Izani Md. Ismail, Joan Goh, Ahmad Abd. Majid

Abstract:

In this paper, collocation based cubic B-spline and extended cubic uniform B-spline method are considered for solving one-dimensional heat equation with a nonlocal initial condition. Finite difference and θ-weighted scheme is used for time and space discretization respectively. The stability of the method is analyzed by the Von Neumann method. Accuracy of the methods is illustrated with an example. The numerical results are obtained and compared with the analytical solutions.

Keywords: heat equation, Collocation based, Cubic Bspline, Extended cubic uniform B-spline

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