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<p>To solve all types of Fredholm integro-differential equations, we develop a computational automation based on the collocation method. <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\gamma \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>γ</mi> </math></EquationSource> </InlineEquation>-spline basis functions are employed to compute an approximate solution of these linear integral equations. In addition, Pocklington’s integro-differential equation is studied in this work. Accordingly, the signal reconstruction in the wire antennas is treated using these equations. Several techniques based on quadrature computational automation methods are involved to determine the computed solutions of the considered integro-differential equations. Moreover, the <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\gamma \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>γ</mi> </math></EquationSource> </InlineEquation>-spline interpolation function is proposed to solve the Fredholm equation. Some examples are presented to indicate the numerical convergence orders <InlineEquation ID="IEq5"> <EquationSource Format="TEX">\(\mathcal {O}(h^{\gamma +1})\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi mathvariant="script">O</mi> <mo stretchy="false">(</mo> <msup> <mi>h</mi> <mrow> <mi>γ</mi> <mo>+</mo> <mn>1</mn> </mrow> </msup> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>, accuracy, effectiveness, and robustness of the method.</p>

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Computational automation for solving Pocklington’s integro-differential equation based on Fredholm integral equations and \(\gamma \)-spline interpolants

  • 期刊论文

  • 发表日期：

    2026年3月7日

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  • Mohamed Addam,
  • Imad El Barkani

摘要

To solve all types of Fredholm integro-differential equations, we develop a computational automation based on the collocation method. \(\gamma \) γ -spline basis functions are employed to compute an approximate solution of these linear integral equations. In addition, Pocklington’s integro-differential equation is studied in this work. Accordingly, the signal reconstruction in the wire antennas is treated using these equations. Several techniques based on quadrature computational automation methods are involved to determine the computed solutions of the considered integro-differential equations. Moreover, the \(\gamma \) γ -spline interpolation function is proposed to solve the Fredholm equation. Some examples are presented to indicate the numerical convergence orders \(\mathcal {O}(h^{\gamma +1})\) O ( h γ + 1 ) , accuracy, effectiveness, and robustness of the method.