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AN EFFICIENT NUMERICAL APPROXIMATION FOR LINEAR AND NONLINEAR FREDHOLM INTEGRO-DIFFERENTIAL EQUATIONS
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Abstract. In this study, we deal with a linear and non-linear Fredholm integro differential equation (FIDE's). Firstly, asymptotic estimates were conducted for the problem under consideration. Then, a finite difference scheme was established using interpolation quadrature rules, basis function, and integral remainder terms. The discrete maximum norm was utilized to evaluate the error estimate. Finally, two test problems were given to demonstrate the effectiveness of the proposed method in solving the Fredholm integro-differential equation, which contains both linear and non-linear terms.
Azerbaijan University of Architecture and Construction
Title: AN EFFICIENT NUMERICAL APPROXIMATION FOR LINEAR AND NONLINEAR FREDHOLM INTEGRO-DIFFERENTIAL EQUATIONS
Description:
Abstract.
In this study, we deal with a linear and non-linear Fredholm integro differential equation (FIDE's).
Firstly, asymptotic estimates were conducted for the problem under consideration.
Then, a finite difference scheme was established using interpolation quadrature rules, basis function, and integral remainder terms.
The discrete maximum norm was utilized to evaluate the error estimate.
Finally, two test problems were given to demonstrate the effectiveness of the proposed method in solving the Fredholm integro-differential equation, which contains both linear and non-linear terms.
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