Abstract: This paper compared the efficiency of Simpson’s 1/3 and 3/8 rules for the numerical solution of first order Volterra integro-differential equations. In developing the solution, collocation approximation method was adopted using the shifted Legendre polynomial as basis function. A block method approach is preferred to the predictor corrector method for being self-starting. Experimental results confirmed that the Simpson’s 3/8 rule is more efficient than the Simpson’s 1/3 rule.
Abstract: Volterra integro-differential equations appear in many models for real life phenomena. Since analytical solutions for this type of differential equations are hard and at times impossible to attain, engineers and scientists resort to numerical solutions that can be made as accurately as possible. Conventionally, numerical methods for ordinary differential equations are adapted to solve Volterra integro-differential equations. In this paper, numerical solution for solving Volterra integro-differential equation using extended trapezoidal method is described. Formulae for the integral and differential parts of the equation are presented. Numerical results show that the extended method is suitable for solving first order Volterra integro-differential equations.
Abstract: Beginning from the creator of integro-differential
equations Volterra, many scientists have investigated these
equations. Classic method for solving integro-differential
equations is the quadratures method that is successfully applied up
today. Unlike these methods, Makroglou applied hybrid methods
that are modified and generalized in this paper and applied to the
numerical solution of Volterra integro-differential equations. The
way for defining the coefficients of the suggested method is also
given.