A variable time step Galerkin method for a one-dimensional Stefan problem

1997 ◽  
Vol 81 (2-3) ◽  
pp. 189-200 ◽  
Author(s):  
N.S. Asaithambi
Keyword(s):  
Galerkin Method ◽  
Stefan Problem ◽  
Time Step ◽  
One Dimensional ◽  
Variable Time ◽  
Variable Time Step

scholarly journals On the Numerical Simulation of HPDEs Using θ-Weighted Scheme and the Galerkin Method

Mathematics ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 78
Author(s):  
Haifa Bin Jebreen ◽  
Fairouz Tchier
Keyword(s):  
Differential Equation ◽  
Galerkin Method ◽  
Linear Ordinary Differential Equation ◽  
Time Interval ◽  
Hyperbolic Partial Differential Equation ◽  
Time Step ◽  
Numerical Examples ◽  
One Dimensional ◽  
The Stability ◽  
The Galerkin Method

Herein, an efficient algorithm is proposed to solve a one-dimensional hyperbolic partial differential equation. To reach an approximate solution, we employ the θ-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 and guarantee the validity of the stability, consistency, and convergence analysis.

An Improved Method of Jiles-Atherton Hysteresis Model Based on Variable Time-Step Simulation

2021 ◽  
Author(s):  
Yinguo Yang ◽  
Liling Xiang ◽  
Yitan Guo ◽  
Zhendong Tan ◽  
Yankan Song
Keyword(s):  
Hysteresis Model ◽  
Improved Method ◽  
Time Step ◽  
Variable Time ◽  
Model Based ◽  
Variable Time Step
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