Orthogonal collocation

Physics

Engineering

Mathematical analysis

Aerospace engineering

Bernoulli's principle

Fractional calculus

Nonlinear system

Boundary value problem

Collocation method

Algebraic equation

Applied mathematics

Mathematics

Ordinary differential equation

Partial derivative

Quantum mechanics

Differential equation

Partial differential equation

Numerical partial differential equations

Numerical Methods for Partial Differential Equations

In this paper, an efficient and accurate numerical method is presented for solving two types of fractional partial differential equations. The fractional derivative is described in the Caputo sense. Our approach is based on Bernoulli wavelets collocation techniques together with the fractional integral operator, described in the Riemann‐Liouville sense. The main characteristic behind this approach is to reduce such problems to those of solving systems of algebraic equations, which greatly simplifies the problem. By using Newton's iterative method, this system is solved and the solution of fractional partial differential equations is achieved. Some results concerning the error analysis are obtained. The validity and applicability of the method are demonstrated by solving four numerical examples. Numerical examples are presented in the form of tables and graphs to make comparisons with the results obtained by other methods and with the exact solutions much easier.

A numerical scheme based on Bernoulli wavelets and collocation method for solving fractional partial differential equations with Dirichlet boundary conditions