A novel third kind Chebyshev wavelet collocation method for the numerical solution of stochastic fractional Volterra integro-differential equations

In the formulation of natural processes like emissions, population development, financial markets, and the mechanical systems, in which the past affect both the present and the future, Volterra integro-differential equations appear. Moreover, as many phenomena in the real world suffer from disturbances or random noise, it is normal and healthy for them to go from probabilistic models to stochastic models. This article introduces a new approach to solve stochastic fractional Volterra integro-differential equations based on the operational matrix method of Chebyshev wavelets of third kind and stochastic operational matrix of Chebyshev wavelets of third kind. Also, we have given the convergence and error analysis of the proposed method. A variety of numerical experiments are carried out to demonstrate our theoretical findings.Publisher's Versio

The numerical solution of singular initial value problems using Chebyshev wavelet collocation method

AbstractWavelet analysis is a recently developed mathematical tool for many problems. In this paper, an efficient and new numerical method is proposed for the numerical solution of singular initial value problems, which is based on collocation points with Chebyshev wavelet. The present method is developed using the Chebyshev wavelet and its operational matrices to obtain higher accuracy. It has been shown here that the present method can be easily implemented and the results obtained are most accurate. Hence the present method has a clear advantage over the classical methods. Numerical order of convergence of the proposed method is calculated. The results show the better accuracy of the proposed method, which is justified through the illustrative examples

Solving Optimal Linear Time-Variant Systems via Chebyshev Wavelet

Over the last four decades, optimal control problem are solved using direct and indirect methods. Direct methods are based on using polynomials to represent the optimal problem. Direct methods can be implemented using either discretization or parameterization. The proposed method here is considered as a direct method in which the optimal control problem is directly converted into a mathematical programming problem. A wavelet-based method is presented to solve the linear quadratic optimal control problem. The Chebyshev wavelets functions are used as the basis functions. Numerical examples are presented to show the effectiveness of the method, several optimal control problems were solved, and the simulation results show that the proposed method gives good and comparable results with some other methods

A technique for solving system of generalized Emden-Fowler equation using Legendre wavelet

This article is concerned with the development of an efficient numerical algorithm for the solution of a system of generalized nonlinear Emden-Fowler equation. The proposed algorithm is based on the Legendre wavelet operational matrix of integration technique. This method decreases the storage and computational complexity due to its calculation on the subinterval [ (n-1)/2^(k-1) , n/2^(k-1)) of [0,1]. The main highlight of this method is to converts the system of the differential equation into an equivalent system of nonlinear algebraic equations, which greatly simplifies approximation. Some numerical example shows that the proposed scheme is very efficient and reliable.Publisher's Versio