Collocation methods based on Gegenbauer and Bernoulli wavelets for solving neutral delay differential equations

Abstract

In this paper, we introduce two different methods based on Gegenbauer wavelet and Bernoulli wavelet for the solution of neutral delay differential equations. These methods convert linear and nonlinear neutral delay differential equations into system of linear and nonlinear algebraic equations, respectively. After solving these equations, we get the approximate solutions. Here, we have used the Gegenbauer wavelet (for different values of μ) and Bernoulli wavelet and seen that both methods converge fast. We present six test problems consisting of five linear and one nonlinear, to illustrate the accuracy of present methods. Further, we compared our results with the results of existing methods present in the literature and have seen that our methods give more accurate results.