%0 Journal Article
	%A Anirut Luadsong and  Nitima Aschariyaphotha
	%D 2011
	%J International Journal of Mathematical and Computational Sciences
	%B World Academy of Science, Engineering and Technology
	%I Open Science Index 54, 2011
	%T The Splitting Upwind Schemes for Spectral Action Balance Equation
	%U https://publications.waset.org/pdf/12679
	%V 54
	%X The spectral action balance equation is an equation that
used to simulate short-crested wind-generated waves in shallow water
areas such as coastal regions and inland waters. This equation consists
of two spatial dimensions, wave direction, and wave frequency which
can be solved by finite difference method. When this equation with
dominating convection term are discretized using central differences,
stability problems occur when the grid spacing is chosen too coarse.
In this paper, we introduce the splitting upwind schemes for avoiding
stability problems and prove that it is consistent to the upwind scheme
with same accuracy. The splitting upwind schemes was adopted
to split the wave spectral action balance equation into four onedimensional
problems, which for each small problem obtains the
independently tridiagonal linear systems. For each smaller system
can be solved by direct or iterative methods at the same time which
is very fast when performed by a multi-processor computer.
	%P 899 - 907