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This document presents a study on the finite difference method applied to solve the space-time fractional wave equation in the Caputo form, discussing aspects of stability and convergence.
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How to fill out finite difference method for

01
Define the domain and discretize it into a grid or mesh.
02
Choose the parameters for time and space steps (delta t and delta x).
03
Identify the partial differential equation (PDE) to be solved.
04
Set up the finite difference approximations for the derivatives in the PDE.
05
Create a system of equations based on the finite difference approximations.
06
Apply boundary and initial conditions to the system of equations.
07
Solve the resulting algebraic equations using appropriate numerical methods.
08
Analyze and interpret the results.

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Academics and students in computational mathematics and numerical analysis.
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The finite difference method is a numerical technique used for approximating solutions to differential equations by using finite difference equations to approximate derivatives.
The finite difference method is generally used by engineers, scientists, and mathematicians who are involved in computational modeling and simulations that require solving differential equations.
To apply the finite difference method, one must discretize the domain into a grid, select appropriate finite difference approximations for the derivatives, and set up a system of equations that can be solved using numerical techniques.
The purpose of the finite difference method is to provide a systematic way to compute numerical solutions to differential equations, which can model a wide range of physical phenomena.
Information that must be reported includes the grid size, the type of finite difference approximations used, boundary conditions, initial conditions, and the results obtained from the computation.
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Relevant keywords

fractional calculus finite difference method fractional wave equation numerical analysis Caputo derivative stability convergence differential equations mathematics wave propagation

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