A fractional B-spline collocation method for the numerical solution of fractional predator-prey models

We present a collocation method based on fractional B-splines for the solution of fractional differential problems. The key-idea is to use the space generated by the fractional B-splines, i.e., piecewise polynomials of noninteger degree, as approximating space. Then, in the collocation step the fractional derivative of the approximating function is approximated accurately and efficiently by an exact differentiation rule that involves the generalized finite difference operator. To show the effectiveness of the method for the solution of nonlinear dynamical systems of fractional order, we solved the fractional Lotka-Volterra model and a fractional predator-pray model with variable coefficients. The numerical tests show that the method we proposed is accurate while keeping a low computational cost

Numerical Solution of Fractional Partial Differential Equations with Normalized Bernstein Wavelet Method

In this paper, normalized Bernstein wavelets are presented. Next, the fractional order integration and Bernstein wavelets operational matrices of integration are derived and finally are used for solving fractional partial differential equations. The operational matrices merged with the collocation method are used in order to convert fractional problems to a number of algebraic equations. In the suggested method the boundary conditions are automatically taken into consideration. An assessment of the error of function approximation based on the normalized Bernstein wavelet is also presented. Some numerical instances are given to manifest the versatility and applicability of the suggested method. Founded numerical results are correlated with the best reported results in the literature and the analytical solutions in order to prove the accuracy and applicability of the suggested method

A Two-Dimensional Chebyshev Wavelet Method for Solving Partial Di erential Equations

In this paper, we introduce a two-dimensional Chebyshev wavelet method (TCWM) for solving partial di erential equations (PDEs) in L2(R) space. In this method, the spatial variables appearing in the PDE each has its own kernel, as well as wavelet coecient for approxi- mating the unknown solution of the equation. The approximated solu- tion of the equation is fast and has higher number of vanishing moments as compared to the Chebyshev wavelet method with only one wavelet coecient for two or more separated kernels for the variables appearing in the PDE

(R1987) Hermite Wavelets Method for System of Linear Differential Equations

In this research paper, we present an accurate technique for solving the system of linear differential equations. Such equations often arise as a result of modeling in many systems and applications of engineering and science. The proposed scheme is based on Hermite wavelets basis functions and operational matrices of integration. The demonstrated scheme is simple as it converts the problem into algebraic matrix equation. To validate the applicability and efficacy of the developed scheme, some illustrative examples are also considered. The results so obtained with the help of the present proposed numerical technique by using Hermite wavelets are observed to be more accurate and favorable in comparison with those by using Haar wavelets