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<p>In this research, new equation in the form Two-dimensional Volterra integrodifferential equation (TDVIDE), which is related of the heat conduction and diffusion problems. Using Runge–Kutta method and Bolck-by-Block method, as the best methods for solving Volterra integral equations, it was possible to obtain the solution of TDVIDE. The problems in heat conduction and diffusionwas also studied. Finally, some numerical results are calculated, when the kernel takes acontinouse kernel. In addition, the error estimate, in each case is computed.</p>

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Two Dimensional Volterra Integrodifferential Equation of Heat Conduction and Diffusion Problems and Its Numerical Solutions

  • 期刊论文

  • 发表日期：

    2025年3月10日

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  • Abeer M. Al-Bugami

摘要

In this research, new equation in the form Two-dimensional Volterra integrodifferential equation (TDVIDE), which is related of the heat conduction and diffusion problems. Using Runge–Kutta method and Bolck-by-Block method, as the best methods for solving Volterra integral equations, it was possible to obtain the solution of TDVIDE. The problems in heat conduction and diffusionwas also studied. Finally, some numerical results are calculated, when the kernel takes acontinouse kernel. In addition, the error estimate, in each case is computed.