Department of Mathematics, Iran University of Science and Technology, Iran, Islamic Republic of
Abstract
This paper present a novel numerical algorithm for the linear one- dimensional heat and wave equation. In this method, a nite dierence approach had been used to discrete the time derivative while cubic spline is applied as an interpolation function in the space dimension. We discuss the accuracy of the method by expanding the equation based on Taylor series and minimize the error. The proposed method has eighth-order accuracy in space and fourth-order accuracy in time variables. From the computational point of view, the solution obtained by this method is in excellent agreement with those obtained by previous works and also it is ecient to use. Numerical examples are given to show the applicability and eciency of the method.
Rashidinia, J., Mohsenyzade, M. (2015). NUMERICAL SOLUTION OF ONE-DIMENSIONAL HEAT AND WAVE EQUATION BY NON-POLYNOMIAL QUINTIC SPLINE. International Journal of Mathematical Modelling & Computations, 5(4 (FALL)), 291-305.
MLA
Jalil Rashidinia; Mohamadreza Mohsenyzade. "NUMERICAL SOLUTION OF ONE-DIMENSIONAL HEAT AND WAVE EQUATION BY NON-POLYNOMIAL QUINTIC SPLINE". International Journal of Mathematical Modelling & Computations, 5, 4 (FALL), 2015, 291-305.
HARVARD
Rashidinia, J., Mohsenyzade, M. (2015). 'NUMERICAL SOLUTION OF ONE-DIMENSIONAL HEAT AND WAVE EQUATION BY NON-POLYNOMIAL QUINTIC SPLINE', International Journal of Mathematical Modelling & Computations, 5(4 (FALL)), pp. 291-305.
VANCOUVER
Rashidinia, J., Mohsenyzade, M. NUMERICAL SOLUTION OF ONE-DIMENSIONAL HEAT AND WAVE EQUATION BY NON-POLYNOMIAL QUINTIC SPLINE. International Journal of Mathematical Modelling & Computations, 2015; 5(4 (FALL)): 291-305.
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