Using Bernstein multi-scaling polynomials to obtain numerical solution of Volterra integral equations system

2020 ◽  
Vol 39 (3) ◽  
Author(s):  
A. R. Yaghoobnia ◽  
R. Ezzati
Keyword(s):  
Numerical Solution ◽  
Integral Equations ◽  
Volterra Integral Equations

scholarly journals Convergence Analysis of Legendre Pseudospectral Scheme for Solving Nonlinear Systems of Volterra Integral Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Emran Tohidi ◽  
O. R. Navid Samadi ◽  
S. Shateyi
Keyword(s):  
Nonlinear Systems ◽  
Theoretical Prediction ◽  
Numerical Solution ◽  
Integral Equations ◽  
Volterra Integral Equations ◽  
Volterra Equations ◽  
Exponential Rate ◽  
Exponential Rate Of Convergence ◽  
Legendre Spectral Method ◽  
Pseudospectral Scheme

We are concerned with the extension of a Legendre spectral method to the numerical solution of nonlinear systems of Volterra integral equations of the second kind. It is proved theoretically that the proposed method converges exponentially provided that the solution is sufficiently smooth. Also, three biological systems which are known as the systems of Lotka-Volterra equations are approximately solved by the presented method. Numerical results confirm the theoretical prediction of the exponential rate of convergence.

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