An Efficient Method Based on Taylor Wavelet for Solving Nonlinear Stratonovich-Volterra Integral Equations
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 fi...
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| Veröffentlicht in: | International journal of applied and computational mathematics 2024-04, Vol.10 (2), Article 67 |
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| creator | Ahmed, Shahid Jahan, Shah |
| description | 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. |
| doi_str_mv | 10.1007/s40819-024-01701-z |
| format | Article |
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J. Appl. Comput. Math</stitle><date>2024-04-01</date><risdate>2024</risdate><volume>10</volume><issue>2</issue><artnum>67</artnum><issn>2349-5103</issn><eissn>2199-5796</eissn><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. 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| subjects | Applications of Mathematics Basis functions Computational Science and Engineering Error analysis Mathematical analysis Mathematical and Computational Physics Mathematical Modeling and Industrial Mathematics Mathematics Mathematics and Statistics Nuclear Energy Operations Research/Decision Theory Original Paper Theoretical Volterra integral equations Wavelet analysis |
| title | An Efficient Method Based on Taylor Wavelet for Solving Nonlinear Stratonovich-Volterra Integral Equations |
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