Modified Newton-Raphson solution for dispersion equation of transition water waves

Modified Newton-Raphson solution for dispersion equation of transition water waves is proposed for practical applications. The wave dispersion equation is a nonlinear equation. Therefore, one has to apply a time-consuming trialand-error method. However, it may be solved by utilizing an iterative technique commonly referred to as Newton-Raphson (NR) iteration technique and Chebyshev approximation, which are used to solve the system of nonlinear equations. Chebyshev approximation has the advantage of requiring less iteration. In this study, a numerical solution model based on utilizing modified NR technique with Chebyshev approximation to determine value of the wave number (k) is developed. It is shown how iteration problems can be solved by modified NR technique with Chebyshev approximation. This computational model is applied by computer programs that have visual basic (VBA) code prepared under the Microsoft Excel Macro. The wave dispersion equation for transition water waves were solved by modified NR technique with Chebyshev approximation implemented in the computer programs prepared with VBA computer language. An example for the given numerical solution model is presented.