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An Efficient Method Based on Taylor Wavelet for Solving Nonlinear Stratonovich-Volterra Integral Equations

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Abstract

In this article, we present an effective technique for solving nonlinear Stratonovich-Volterra integral equations. The technique is based on Taylor wavelet to construct the operational matrix of integration (OMI) and the stochastic OMI. These matrices allow us to approximate the equations using a finite number of basis functions. By employing these operational matrices, we discretize the integral equations and transform them into a set of algebraic equations, which can be solved using Newton’s method. Further, we conduct error analysis, perform numerical simulations, and present the corresponding results to establish the credibility and practical applicability of the proposed technique. To demonstrate the precision and accuracy of our approach, we compare our results with those obtained using block pulse functions and the Legendre wavelet method. Numerical examples are provided to show the efficiency of our approach.

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Acknowledgements

We would like to thank Central University of Haryana for providing necessary facilities to carry out this research. We are grateful to the anonymous referees for their comments and valuable suggestions that improved this paper.

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  1. Department of Mathematics, Central University of Haryana, Mahendragarh, 123029, India

    Shahid Ahmed & Shah Jahan

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  1. Shahid Ahmed
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  2. Shah Jahan
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Correspondence to Shah Jahan.

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Ahmed, S., Jahan, S. An Efficient Method Based on Taylor Wavelet for Solving Nonlinear Stratonovich-Volterra Integral Equations. Int. J. Appl. Comput. Math 10, 67 (2024). https://doi.org/10.1007/s40819-024-01701-z

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