On the Numerical Simulation of HPDEs Using theta-Weighted Scheme and the Galerkin Method
Fairouz, Bin Jebreen, Haifa; Tchier, . 2021
Herein, an efficient algorithm is proposed to solve a one-dimensional hyperbolic partial differential equation. To reach an approximate solution, we employ the theta-weighted scheme to discretize the time interval into a finite number of time steps. In each step, we have a linear ordinary differential equation. Applying the Galerkin method based on interpolating scaling functions, we can solve this ODE. Therefore, in each time step, the solution can be found as a continuous function. Stability, consistency, and convergence of the proposed method are investigated. Several numerical examples are devoted to show the accuracy and efficiency of the method
Systems of high-dimensional nonlinear ordinary differential equations play a significant
role in Physics and applied sciences including big-data optimization, financial models, epidemic…