The Simpson’s 3/8 rule is used to solve the nonlinear Volterra integral equations system. Using this rule the system is converted to a nonlinear block system and then by solving this nonlinear system we find approximate solution of nonlinear Volterra integral equations system. One of the advantages of the proposed method is its simplicity in application. Further, we investigate the convergence of the proposed method and it is shown that its convergence is of order
We consider the system of second kind Volterra integral equations (VIE) given by
In recent years, application of HPM (Homotopy Perturbation Method) and ADM (Adomian Decomposition Method) in nonlinear problems has been undertaken by several scientists and engineers [
In this paper, we consider block by block method by using Simpson's
This paper is organized as follow: in Section
Consider a system of nonlinear Volterra integral equations in (
Consider the system of VIE
By setting
In this section we investigate the convergence of the proposed method. The following theorem shows that the order of convergence is at least four.
The approximate method given by the systems Equations (
We have
In this section, some examples are given to certify the convergence and error bounds of the presented method. All results are computed using the well-known symbolic software Maple 12. Tables
Numerical results of Example
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Numerical results of Example
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Numerical results of Example
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Numerical results of Example
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Numerical results of Example
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Numerical results of Example
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Consider the following system [
Consider the following system [
Consider the following system [
Consider the following system [
Consider the following Volterra system of integral equations [
Consider the following Volterra system of integral equations [
Now let
Note that in the Table
This paper was prepared when the third author visits the Institute for Mathematical Research (INSPEM) thus the authors wish to thank the Institute for Mathematical Research (INSPEM), University Putra Malaysia. The authors would also like to express their sincere thanks and gratitude to the reviewer(s) for their valuable comments and suggestions.