A Numerical Method for Solving Volterra Integral Equations with Oscillatory Kernels Using a Transform

2021 ◽  
Vol 14 (4) ◽  
pp. 379-387
Author(s):  
M. Uddin ◽  
A. Khan
Keyword(s):  
Numerical Method ◽  
Integral Equations ◽  
Volterra Integral Equations

scholarly journals Orthonormal Bernstein polynomials for Volterra integral equations of the second kind

2020 ◽  
Vol 9 (1) ◽  
pp. 9
Author(s):  
Jafar Biazar ◽  
Hamed Ebrahimi
Keyword(s):  
Mathematical Modeling ◽  
Integral Equation ◽  
Numerical Method ◽  
Integral Equations ◽  
Method Of Moments ◽  
Volterra Integral Equation ◽  
Bernstein Polynomials ◽  
Volterra Integral Equations ◽  
Linear Volterra Integral Equations ◽  
Relative Errors

The purpose of this research is to provide an effective numerical method for solving linear Volterra integral equations of the second kind. The mathematical modeling of many phenomena in various branches of sciences lead into an integral equation. The proposed approach is based on the method of moments (Galerkin- Ritz) using orthonormal Bernstein polynomials. To solve a Volterra integral equation, the ap-proximation for a solution is considered as an expansion in terms of Bernstein orthonormal polynomials. Ultimately, the usefulness and extraordinary accuracy of the proposed approach will be verified by a few examples where the results are plotted in diagrams, Also the re-sults and relative errors are presented in some Tables.  

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