Exponentially Fitted Diagonally Implicit EDITRK Method for Solving ODEs

Authors

Firas A. Fawzi Department of Mathematics, Faculty of Computer Science and Mathematics, Tikrit University, Sallah AL-Deen, IRAQ
Nour W. Jaleel Department of Mathematics,Faculty of Computer Science and Mathematics ,University of Tikrit

DOI:

https://doi.org/10.30526/36.1.2883

Keywords:

Numerical Methods, Exponentially Fitted, Ordinary Differential Equations, Diagonal Implicit Type Runge Kutta Methods

Abstract

This paper derives the EDITRK4 technique, which is an exponentially fitted diagonally implicit RK method for solving ODEs . This approach is intended to integrate exactly initial value problems (IVPs), their solutions consist of linear combinations of the group functions and for exponentially fitting problems, with being the problem’s major frequency utilized to improve the precision of the method. The modified method EDITRK4 is a new three-stage fourth-order exponentially-fitted diagonally implicit approach for solving IVPs with functions that are exponential as solutions. Different forms of -order ODEs must be derived using the modified system, and when the same issue is reduced to a framework of equations that can be solved using conventional RK approaches, numerical comparisons must be done. The findings show that the novel approach is more efficacious than previously published methods.

Author Biographies

Firas A. Fawzi, Department of Mathematics, Faculty of Computer Science and Mathematics, Tikrit University, Sallah AL-Deen, IRAQ
Nour W. Jaleel, Department of Mathematics,Faculty of Computer Science and Mathematics ,University of Tikrit

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