Bernoulli Matrix Approach for Solving Two Dimensional Linear Hyperbolic Partial Differential Equations with Constant Coefficients

The purpose of this study is to give a Bernoulli polynomial approximation for thesolution of hyperbolic partial differential equations with three variables and constant coefficients. For this purpose, a Bernoulli matrix approach is introduced. This method is based on taking the truncated Bernoulli expansions of the functions in the partial differential equations. After replacing the approximations of functions in the basic equation, we deal with a linear algebraic equation. Hence, the result matrix equation can be solved and the unknown Bernoulli coefficients can be found approximately. The efficiency of the proposed approach is demonstrated with one example.