Development of Variable Stepsize Variable Order Block Method in Divided Difference Form for the Numerical Solution of Delay Differential Equations
This paper considers the development of a two-point
predictor-corrector block method for solving delay differential
equations. The formulae are represented in divided difference form
and the algorithm is implemented in variable stepsize variable order
technique. The block method produces two new values at a single
integration step. Numerical results are compared with existing
methods and it is evident that the block method performs very well.
Stability regions of the block method are also investigated.
block method, delay differential equations,
predictor-corrector, stability region, variable stepsize variable order.
Development of Extended Trapezoidal Method for Numerical Solution of Volterra Integro-Differential Equations
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.
Accuracy, extended trapezoidal method, numerical solution, Volterra integro-differential equations.