Abstract
In this paper, a hybrid of Finite difference-Simpson’s approach was applied to solve linear Volterra integro-differential equations. The method works efficiently great by reducing the problem into a system of linear algebraic equations. The numerical results shows the simplicity and effectiveness of the method, error estimation of the method is provided which shows that the method is of second order convergence.
Highlights
V ito Volterra in 1926 introduced integro-differential for the first time when he investigated the population growth, focussing his study on the hereditary influences, whereby through his research work the topic of integro-differential equations was established [1]
The proposed method of finite difference-Simpson’s approach is used to obtain the numerical solutions of problems of LVIDES in order to study the performance of the method
We compare the results obtained by using our method and numerical method of Romberg extrapolation algorithm (REA) given in [13]
Summary
V ito Volterra in 1926 introduced integro-differential for the first time when he investigated the population growth, focussing his study on the hereditary influences, whereby through his research work the topic of integro-differential equations was established [1]. Mathematical modeling of real life problems often result in functional equations such as differential, integral and integro-differential equations. Many mathematical formulation of physical phenomena reduced to integro-differential equations like fluid dynamics, control theory, biological models and chemical kinetics [1–8]. Linear Integro-Differential Equation (LIDE) is an important branch of modern mathematics and arises often in many applied areas which include engineering, mechanics, physics, chemistry, astronomy, biology, economics, potential theory and electrostatics [9]. A variational iteration method and trapezoidal rule by Saadati et al, [10] was used for solving LIDEs. Manafianheris [11] applied modified laplace Adomian decomposition method.
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