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<p>This study investigates the approximation of solution functions for a system of Volterra integral equations using partial sums of their first-kind Chebyshev wavelet expansions within the interval <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\([0,\gamma )\)</EquationSource> </InlineEquation>, where <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\gamma &gt;0\)</EquationSource> </InlineEquation>. The solutions are obtained using first-kind Chebyshev wavelets. These wavelet-based solutions demonstrate excellent agreement with the exact analytical solutions and are better than other numerical methods signifying the efficiency of the method. The convergence analysis results are also obtained showing the rate of approximation. This result signifies a notable advancement in wavelet analysis and underscores the efficacy of the Chebyshev wavelet method in addressing integral equations.</p>

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First Kind Chebyshev Wavelets’ Approximation of Solution Function of the System of Volterra Integral Equations in Hölder’s Class

  • 期刊论文

  • 发表日期：

    2026年3月30日

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  • Harish Chandra Yadav,
  • Abhilasha Yadav

摘要

This study investigates the approximation of solution functions for a system of Volterra integral equations using partial sums of their first-kind Chebyshev wavelet expansions within the interval \([0,\gamma )\) , where \(\gamma >0\) . The solutions are obtained using first-kind Chebyshev wavelets. These wavelet-based solutions demonstrate excellent agreement with the exact analytical solutions and are better than other numerical methods signifying the efficiency of the method. The convergence analysis results are also obtained showing the rate of approximation. This result signifies a notable advancement in wavelet analysis and underscores the efficacy of the Chebyshev wavelet method in addressing integral equations.