Research Article
Year 2020,
Volume: 16 Issue: 4, 393 - 401, 30.12.2020
Abstract
References
- 1. Wazwaz, AM. Linear and Nonlinear Integral Equations Higher Education Press, Springer-Verlag, Beijing, Berlin, Heidelberg, 2011; pp 639.
- 2. Kolmanovskii, V, Myshkis, A. Introduction to the Theory and Applications of Functional Differential Equations. Kluger Academic Publishers, Dordrecht, Boston, London, 1999; pp 278.
- 3. Oğuz, C, Sezer. M. 2015. Chelyshkov collocation method for a class of mixed functional integro-differential equations. Applied Mathematics and Computation; 259: 943-954.
- 4. Farshid, M, Bimesl, S, Tohidi, E. 2016. A numerical framework for solving high-order pantograph-delay Volterra integro-differential equations. Kuwait Journal of Science; 43.1.
- 5. Kürkçü, ÖK, Aslan, E, Sezer, M. 2016. A numerical approach with error estimation to solve general integro-differential–difference equations using Dickson polynomials. Applied Mathematics and Computation; 276: 324-339.
- 6. Yüzbaşı, Ş. 2014. Laguerre approach for solving pantograph-type Volterra integro-differential equations. Applied Mathematics and Computation; 232: 1183-1199.
- 7. Reutskiy, SY. 2016. The backward substitution method for multipoint problems with linear Volterra–Fredholm integro-differential equations of the neutral type. Journal of Computational and Applied Mathematics; 296: 724-738.
- 8. Bahşı, MM, Çevik, M, Kurt Bahşı A, Sezer M. 2016. Improved Jacobi Matrix Method for the numerical solution Fredholm Integro-Differential-Difference Equations. Mathematical Sciences.
- 9. Bahşı, MM, Çevik M, Sezer M. 2018. Jacobi polynomial solutions of Volterra integro-differential equations with weakly singular kernel. New Trends in Mathematical Sciences; 6.3: 24-38.
- 10. Şahin, M, Sezer, M. 2018. Pell-Lucas Collocation Method for Solving High-Order Functional Differential Equations with Hybrid Delays. Celal Bayar Üniversitesi Fen Bilimleri Dergisi; 14.2: 141-149.
- 11. Bellour, A, Bousselsal, M. 2014. Numerical solution of delay integro‐differential equations by using Taylor collocation method. Mathematical Methods in the Applied Sciences; 37.10: 1491-1506.
- 12. Vilmoš H. On Polynomial Spline Collocation Methods for Neutral Volterra Integro–Differential Equations with Delay Arguments. Proceedings of the 1. Conference on Applied Mathematics and Computation, Dubrovnik, Croatia, 1999.
Improved Jacobi Matrix Method for Solving Multi-Functional Integro-Differential Equations with Mixed Delays
Abstract
In this study, we suggested a novel approach for solving multi-functional integro-differential equations with mixed delays, by using orthogonal Jacobi polynomials. These equations include various classes of differential equations, integro-differential equations and delay differential equations. This new algorithm proposes solutions for each class of these equations and combinations of equation classes, such as Volterra integro-differential equation, Fredholm integro-differential equation, pantograph-delay differential equations. Since the present method is based on fundamental matrix relations and collocation points, numerical solutions can be obtained easily by means of symbolic computation programs. We developed an error estimation algorithm based on the present method for the verification of solutions. Application of the method is illustrated by four numerical examples.
References
- 1. Wazwaz, AM. Linear and Nonlinear Integral Equations Higher Education Press, Springer-Verlag, Beijing, Berlin, Heidelberg, 2011; pp 639.
- 2. Kolmanovskii, V, Myshkis, A. Introduction to the Theory and Applications of Functional Differential Equations. Kluger Academic Publishers, Dordrecht, Boston, London, 1999; pp 278.
- 3. Oğuz, C, Sezer. M. 2015. Chelyshkov collocation method for a class of mixed functional integro-differential equations. Applied Mathematics and Computation; 259: 943-954.
- 4. Farshid, M, Bimesl, S, Tohidi, E. 2016. A numerical framework for solving high-order pantograph-delay Volterra integro-differential equations. Kuwait Journal of Science; 43.1.
- 5. Kürkçü, ÖK, Aslan, E, Sezer, M. 2016. A numerical approach with error estimation to solve general integro-differential–difference equations using Dickson polynomials. Applied Mathematics and Computation; 276: 324-339.
- 6. Yüzbaşı, Ş. 2014. Laguerre approach for solving pantograph-type Volterra integro-differential equations. Applied Mathematics and Computation; 232: 1183-1199.
- 7. Reutskiy, SY. 2016. The backward substitution method for multipoint problems with linear Volterra–Fredholm integro-differential equations of the neutral type. Journal of Computational and Applied Mathematics; 296: 724-738.
- 8. Bahşı, MM, Çevik, M, Kurt Bahşı A, Sezer M. 2016. Improved Jacobi Matrix Method for the numerical solution Fredholm Integro-Differential-Difference Equations. Mathematical Sciences.
- 9. Bahşı, MM, Çevik M, Sezer M. 2018. Jacobi polynomial solutions of Volterra integro-differential equations with weakly singular kernel. New Trends in Mathematical Sciences; 6.3: 24-38.
- 10. Şahin, M, Sezer, M. 2018. Pell-Lucas Collocation Method for Solving High-Order Functional Differential Equations with Hybrid Delays. Celal Bayar Üniversitesi Fen Bilimleri Dergisi; 14.2: 141-149.
- 11. Bellour, A, Bousselsal, M. 2014. Numerical solution of delay integro‐differential equations by using Taylor collocation method. Mathematical Methods in the Applied Sciences; 37.10: 1491-1506.
- 12. Vilmoš H. On Polynomial Spline Collocation Methods for Neutral Volterra Integro–Differential Equations with Delay Arguments. Proceedings of the 1. Conference on Applied Mathematics and Computation, Dubrovnik, Croatia, 1999.
There are 12 citations in total.
Details
| Primary Language | English |
|---|---|
| Subjects | Engineering |
| Journal Section | Articles |
| Authors | |
| Publication Date | December 30, 2020 |
| Published in Issue | Year 2020 Volume: 16 Issue: 4 |
