Wave shoaling and the angular frequency is proportional to its local rate of change, Simplifying to one dimension and cross-differentiating it is now easily seen that the above definitions indicate simply that the rate of change of wavenumber is balanced by the convergence of the frequency along a ray; Assuming stationary conditions (formula_27), this implies that wave crests are conserved and the frequency must remain constant along a wave ray as formula_28. As waves enter shallower waters, the decrease in group velocity caused by the reduction in water depth leads to a reduction in wave length formula_29 because the nondispersive shallow water
Successive over-relaxation methods were designed for computation by human calculators, and they required some expertise to ensure convergence to the solution which made them inapplicable for programming on digital computers. These aspects are discussed in the thesis of David M. Young, Jr. Given a square system of "n" linear equations with unknown x: where: Then "A" can be decomposed into a diagonal component "D", and strictly lower and upper triangular components "L" and "U": where The system of linear equations may be rewritten as: for a constant "ω" > 1, called the "relaxation factor". The method of successive over-relaxation is an iterative