Quantum mechanics

Discretization

Applied mathematics

Computer science

Algebraic equation

Physics

Nonlinear system

Mathematics

Mathematical analysis

Geometry

Partial differential equation

Artificial neural network

Fractional calculus

Finite difference method

Machine learning

Finite difference

Radial basis function

Sine

Computational and Applied Mathematics

One of the most powerful tools for solving partial differential equations is approximation using the radial basis functions (RBFs). This method can be very spectrally accurate because it is meshfree. This paper presents a semi-discretization numerical scheme to solve the stochastic coupled nonlinear time fractional sine-Gordon equations, which are obtained by replacing integer time derivative with the Caputo fractional time derivative of order $$\alpha $$ α ( $$1<\alpha \le 2$$ 1 < α ≤ 2 ) and adding stochastic factors. Using this method, the stochastic coupled nonlinear time fractional sine-Gordon equation is transformed to a system of nonlinear algebraic equations that can be solved by a suitable numerical method. This method is a combination of finite difference (FD) method and RBFs. First, time is overcome by forward FD method, then in the direction of space using the meshless method based on RBFs, the unknown function is approximated. This method is very practical, accurate and appropriate. Finally, two examples show the accuracy and efficiency of the proposed method.

Application of combination schemes based on radial basis functions and finite difference to solve stochastic coupled nonlinear time fractional sine-Gordon equations