Numerical Solution of a New Type Fuzzy Nonlinear Volterra Integral Equations

Theory of Approximation and Applications

دوره 16، شماره 1، مرداد 2022، صفحه 81-91   

نوع مقاله: Research Articles

نویسنده

Laleh Hooshangian^*

Department of Mathematics, Dezful Branch, Islamic Azad University, Dezful, Iran.

چکیده

Fuzzy integral equations play a fundamental role in the many fields of engineering and applied mathematics.
The paper presented, a new type of fuzzy Volterra integral equations of the  second kind with nonlinear fuzzy
kernels. Numerical solutions of a new type of nonlinear fuzzy Volterra integral equations with nonlinear fuzzy kernels through Variational Homotopy perturbation (VHP) method based on the parametric form of a fuzzy number, is investigated. To find the approximate solution and to get an approximation for fuzzy solution of the new type of nonlinear fuzzy Volterra integral equations the VHPM is applied, and it is shown that VHPM is an effective and reliable approach to solve these equations. Finally, a few numerical examples are given and results unfold that VHPM is very close to exact solutions. The obtained approximate solutions are contrasted with the exact solution, and absolute error between obtaining numerical results and an exact solution are found. One of the examples shows a comparison between VHPM and HPM.

کلیدواژه‌ها

Variational Homotopy perturbation method, Fuzzy Volterra integral equation؛ Nonlinear fuzzy kernels