Discretization method for the numerical solution of 2D Volterra integral equation based on two-dimensional Bernstein polynomial

Faheem Khan; Muhammad Omar; Zafar Ullah

doi:10.1063/1.5051113

journal article·2018-12Open access

Discretization method for the numerical solution of 2D Volterra integral equation based on two-dimensional Bernstein polynomial

Faheem Khan, Muhammad Omar, Zafar Ullah

AIP Advances· Volume 8· Issue 12

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Source abstract

Abstract

This paper develops a numerical technique for the solution of 2D Volterra Integral Equations (2DVIEs). The proposed method is based on the discretization of 2DVIEs by using two-dimensional Bernstein’s approximation. Some results are developed regarding convergence analysis which shows that the given technique converges to the exact solution rapidly. Several examples are also presented to demonstrate the efficiency and accuracy of the proposed method.

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Research context

OpenAlex topics: Fractional Differential Equations Solutions · Iterative Methods for Nonlinear Equations · Numerical methods in inverse problems

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Affiliations

Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan

Department of Mathematics, COMSATS University Islamabad, Islamabad 57000, Pakistan

Department of Mathematics, University of Education, Lahore 32200, Pakistan

References (20)

Show source-provided references

1. Beltyukov B. A. · Differential Equations · 1976 · 12 · 1163

2. Brunner H. · IMA Journal of Numerical Analysis · 1989 · 18 · 61

3. 10.1016/0096-3003(94)90050-710.1016/0096-3003(94)90050-7 ↗

4. 10.1016/s0096-3003(99)00036-310.1016/s0096-3003(99)00036-3 ↗

5. 10.1016/j.amc.2004.04.11810.1016/j.amc.2004.04.118 ↗

6. 10.1080/0020716070122471210.1080/00207160701224712 ↗

7. Hou J. · 2010 · 427

8. 10.1016/j.cnsns.2010.05.00610.1016/j.cnsns.2010.05.006 ↗

9. 10.1007/s13370-014-0283-610.1007/s13370-014-0283-6 ↗

10. 10.22401/jnus.11.3.1710.22401/jnus.11.3.17 ↗

11. 10.1063/1.489833110.1063/1.4898331 ↗

12. 10.12732/ijpam.v98i4.810.12732/ijpam.v98i4.8 ↗

13. 10.1063/1.500881810.1063/1.5008818 ↗

14. 10.1016/j.matcom.2005.02.03510.1016/j.matcom.2005.02.035 ↗

15. 10.22401/jnus.11.3.1710.22401/jnus.11.3.17 ↗

16. Muna Mustafa M. · Mathematical Theory and Modeling · 2014

17. 10.1007/s12043-016-1239-110.1007/s12043-016-1239-1 ↗

18. Ferin G. · 2002

19. Salmon D. · 1988

20. Heitzinger C. · 2003 · 702