Abstract
This paper presents 2-step p-th order (p = 2,3,4) multi-step methods that are based on the combination of both polynomial and exponential functions for the solution of Delay Differential Equations (DDEs). Furthermore, the delay argument is approximated using the Lagrange interpolation. The local truncation errors and stability polynomials for each order are derived. The Local Grid Search Algorithm (LGSA) is used to determine the stability regions of the method. Moreover, applicability and suitability of the method have been demonstrated by some numerical examples of DDEs with constant delay, time dependent and state dependent delays. The numerical results are compared with the theoretical solution as well as the existing Rational Multi-step Method2 (RMM2).
Highlights
This paper presents 2-step p-th order (p = 2, 3, 4) multi-step methods that are based on the combination of both polynomial and exponential functions for the solution of Delay Differential Equations (DDEs)
We present the 2-step p-th order (p = 2, 3, 4) multi-step method for solving DDEs
By taking the step-size h = 0.01in the above examples, the absolute errors by using EPMM and Rational Multi-step Method2 (RMM2) are given in Tables 1 – 3 and their corresponding error graphs are shown in Figures 4 – 6
Summary
Block method for solving Pantograph type functional DDEs was described by Shaalini & Fadugba / J. We present the 2-step p-th order (p = 2, 3, 4) multi-step method for solving DDEs. This method has been referred here as EPMM (2, p), (p = 2, 3, 4). For 2-step p-th order EPMM, let us assume an approximation to the analytical solution y (tn+2) of (1) given by p yn+2 = a0e2h + 1 + b jh j, (2)
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