NUMERICAL SOLUTION OF ONE-DIMENSIONAL HEAT AND WAVE EQUATION BY NON-POLYNOMIAL QUINTIC SPLINE

Subject Areas : International Journal of Mathematical Modelling & Computations

Jalil Rashidinia ¹ , Mohamadreza Mohsenyzade ²

1 - Department of Mathematics, Iran University of Science and Technology, Iran, Islamic Republic of
2 -

Received: 2016-04-15 Accepted : 2016-04-15 Published : 2015-03-21

Keywords: Dierential Equation, Quintic Spline, Heat Equation, Wave Equation, Taylor Approximation,

Abstract :

This paper present a novel numerical algorithm for the linear one-dimensional heat and wave equation. In this method, a nite dierenceapproach had been used to discrete the time derivative while cubic spline isapplied as an interpolation function in the space dimension. We discuss theaccuracy of the method by expanding the equation based on Taylor series andminimize the error. The proposed method has eighth-order accuracy in spaceand fourth-order accuracy in time variables. From the computational pointof view, the solution obtained by this method is in excellent agreement withthose obtained by previous works and also it is ecient to use. Numericalexamples are given to show the applicability and eciency of the method.