Solving Volterra Integral Equations of the Second Kind with Convolution Kernel
سال انتشار: 1400
نوع سند: مقاله ژورنالی
زبان: انگلیسی
مشاهده: 49
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شناسه ملی سند علمی:
JR_IJIM-13-1_006
تاریخ نمایه سازی: 26 دی 1402
چکیده مقاله:
In this paper, we present an approximate method to solve the solution of the second kind Volterra integral equations. This method is based on a previous scheme, applied by Maleknejad et al., [K. Maleknejad and Aghazadeh, Numerical solution of Volterra integral equations of the second kind with convolution kernel by using Taylor-series expansion method, Appl. Math. Comput. (۲۰۰۵)] to gain the approximate solution of the second kind Volterra integral equations with convolution kernel and Maleknejad et al. [K. Maleknejad and T. Damercheli, Improving the accuracy of solutions of the linear second kind volterra integral equations system by using the Taylor expansion method, Indian J. Pure Appl. Math. (۲۰۱۴)] to gain the approximate solutions of systems of second kind Volterra integral equations with the help of Taylor expansion method. The Taylor expansion method transforms the integral equation into a linear ordinary differential equation (ODE) which, in this case, requires specified boundary conditions. Boundary conditions can be determined using the integration technique instead of differentiation technique. This method is more stable than derivative method and can be implemented to obtain an approximate solution of the Volterra integral equation with smooth and weakly singular kernels. An error analysis for the method is provided. A comparison between our obtained results and the previous results is made which shows that the suggested method is accurate enough and more stable.
کلیدواژه ها:
نویسندگان
M. S. Barikbin
Department of Mathematics, Yadegar-e-Emam Khomeyni (RAH) Shahr-e-Rey Branch, Islamic Azad University, Tehran, Iran.
A. R. Vahidi
Department of Mathematics, Yadegar-e-Emam Khomeyni (RAH) Shahr-e-Rey Branch, Islamic Azad University, Tehran, Iran.
T. Damercheli
Department of Mathematics, Yadegar-e-Emam Khomeyni (RAH) Shahr-e-Rey Branch, Islamic Azad University, Tehran, Iran.
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