Numerical approaches to Jimbo-Miwa equation

In this thesis study, the best numerical approximation methods are investigated by applying three methods to Jimbo-Miwa equation which is used to define nonlinear (3+1) dimensional waves. The first of these methods is the Lagrange multiplier method. By Lagrange multiplier method, non-linear Jimbo-Miwa equation is transformed into a linear problem. Finally approximate and analytical solutions are obtained. The second method is the Parameter expansion method. In order to analyze non-linear differential equations with this method, the extension of the dependable variables in the power series with a small parameter is defined and results in the addition of linear differential equations which can be formed consecutively. Finally, the third derivation matrix was used with method is Legendre wavelet method. The differential equation considered under initial conditions is converted to the system of equations and the numerical solution is found by using the functional approach with the coefficients obtained from this system of equation. Besides that, the results of the methods applied to Jimbo-Miwa equation were compared with the other methods and the best numerical solution was discussed.