Optimized Trigonometric Spline Function with Conjugate GradientMethod for Solving FDEs

Hamasalh, Faraidun; Sadiq, Gulnar W.; Salam, Emad S.

doi:10.37652/juaps.2022.176477

Authors

¹ Department of Mathematics, College of Education, University of Sulaimani, Sulaimani, Iraq

² Department of Mathematical Sciences, College of Basic Education, University of Sulaimani, Sulaimani, Iraq

³ University of Sulaimani, Sulaimani, Iraq

10.37652/juaps.2022.176477

Abstract

We investigate the non-polynomial spline function to solve the fractional differential equations with the conformable conjugate gradient method. The fractional derivative was described using the Caputo fractional derivative to construct the spline scheme with polynomial fractional order. Therefore, transform the problem to an equivalent iterative linear system that can be solved by Gauss-Seidel and conjugate gradient methods. For the given spline function, error bounds were studied and a stability analysis was completed, the error estimation is also calculated as different values of (n) depend on the step size oh (h). Numerical examples with known analytical solutions are shown to verify the method's accuracy. The outcomes are in satisfactory correlation with the exact answers according to the numerical experiments. Moreover, the convergence analysis was investigated with the drive some theorems. Also, the procedure is explained in depth and supported by computational examples and the results show that the fractional spline function which interpolates data is productive and profitable in solving unique problems and compare with the exact solutions.

Keywords

Main Subjects

Mathematical

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Journal of University of Anbar for Pure Science

Optimized Trigonometric Spline Function with Conjugate GradientMethod for Solving FDEs

References

References

Volume 16, Issue 2 - Issue Serial Number 2
December 2022
Page 84-91

Optimized Trigonometric Spline Function with Conjugate GradientMethod for Solving FDEs

References

References

Volume 16, Issue 2 - Issue Serial Number 2December 2022Page 84-91

Volume 16, Issue 2 - Issue Serial Number 2
December 2022
Page 84-91