Wavelet collocation methods for solving neutral delay differential equations

Spline Collocation Methods for Solving Second Order Neutral Delay Differential Equations

The aim of this paper is to solve the second order neutral delay differential equations (NDDEs) based on seventh C3-spline collocation methods with three parameters c1, c2, c3 ∈ (0, 1). It is shown that the proposed methods for second order NDDEs possess a convergence rate of order seven if : 1− c1 − c2 − c3 + c1c2 + c1c3 + c2c3 − 2c1c2c3 ≤ 0. Numerical results illustrating the behavior of the ...

Wavelet Collocation Method for Solving Multiorder Fractional Differential Equations

The operational matrices of fractional-order integration for the Legendre and Chebyshev wavelets are derived. Block pulse functions and collocation method are employed to derive a general procedure for forming these matrices for both the Legendre and the Chebyshev wavelets. Then numerical methods based on wavelet expansion and these operational matrices are proposed. In this proposed method, by...

Discrete Collocation Method for Solving Fredholm Volterra Intergro-Differential Equations

Quintic C-Spline Collocation Methods for Stiff Delay Differential Equations

In this paper, a new difference scheme based on C1-quintic splines is derived for the numerical solution of the stiff delay differential equations. Convergence results shows that the methods have a convergence of order five. Moreover, the stability analysis properties of these methods have been studied. Finally, numerical results illustrating the behavior of the methods when faced with some dif...

The Legendre Wavelet Method for Solving Singular Integro-differential Equations

In this paper, we present Legendre wavelet method to obtain numerical solution of a singular integro-differential equation. The singularity is assumed to be of the Cauchy type. The numerical results obtained by the present method compare favorably with those obtained by various Galerkin methods earlier in the literature.