scholarly journals Fourth Order Compact Finite Difference Method for Solving One Dimensional Wave Equation

2016 ◽  
Vol 8 (4) ◽  
pp. 30-30
Author(s):  
Gemechis File Duressa ◽  
Tesfaye Aga Bullo ◽  
Gashu Gadisa Kiltu
Keyword(s):  
Wave Equation ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Fourth Order ◽  
Difference Method ◽  
Compact Finite Difference ◽  
One Dimensional ◽  
Compact Finite Difference Method ◽  
Dimensional Wave

scholarly journals Numerical Computation and Stability Analysis for the Fractional Subdiffusions with Spatial Variable Coefficients

2019 ◽  
Vol 2019 ◽  
pp. 1-14 ◽  
Author(s):  
Lei Ren
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Fourth Order ◽  
Difference Method ◽  
Variable Coefficients ◽  
Finite Difference Approximation ◽  
Difference Approximation ◽  
Approximation Formula ◽  
Compact Finite Difference ◽  
Compact Finite Difference Method

In this paper, we propose an efficient compact finite difference method for a class of time-fractional subdiffusion equations with spatially variable coefficients. Based on the L2-1σ approximation formula of the time-fractional derivative and a fourth-order compact finite difference approximation to the spatial derivative, an efficient compact finite difference method is developed. The local truncation error and the solvability of the developed method are discussed in detail. The unconditional stability of the resulting scheme and also its convergence of second-order in time and fourth-order in space are rigorously proved using a discrete energy analysis method. Numerical examples are provided to demonstrate the accuracy and the theoretical results.

APPLICATION OF A NUMERICAL-ANALYTICAL METHOD FOR SOLVING A ONE-DIMENSIONAL WAVE EQUATION

Akustika ◽  
2021 ◽  
pp. 22
Author(s):  
Vladimir Mondrus ◽  
Dmitrii Sizov
Keyword(s):  
Wave Propagation ◽  
Wave Equation ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Analytical Method ◽  
One Dimensional ◽  
Numerical Analytical Method ◽  
The Finite Difference Method ◽  
Dimensional Wave

The article contains a solution to the problem of wave propagation in a one-dimensional rod from the initial impact. A numerical-analytical method is used to solve the problem. The numerical part of the method is based on the application of the idea of the finite difference method. The analytical part uses the concept of Green’s function to solve the problem in terms of the spatial coordinate in the considered area. The results include graphs of the solution obtained at different points in time.

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