In this paper we develop a coefficient matrix to be used in numerical approximation methods which model the wave equation in two dimensions. In particular, we will briefly introduce the centered difference approximation method. Next, we explain the derivation of the system of equations into which the problem is transformed in order to utilize such a method. Then, we introduce a set of rules to generate the generalized coefficient matrix for use in approximating the wave equation for any number of unknowns per axis. Finally, we write MATLAB code which uses our matrix to solve said approximations, and then use it in a real world application. The desired outcome of this project has been achieved: to generalize the coefficient matrix used in the system of equations which approximates the wave equation in two dimensions so that its algorithm may be used in MATLAB code for any number of unknowns.
Brown, Morgan M.
"Identifying a Coefficient Matrix for Numerical Approximations to the Wave Equation in Two Dimensions,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 16:
1, Article 9.
Available at: https://scholar.rose-hulman.edu/rhumj/vol16/iss1/9