  Chebyshev pseudospectral (PS) methods are reported to provide highly accurate
solution using polynomial approximation. Use of polynomial basis functions in
PS algorithms limits the formulation to univariate systems constraining it to
tensor product grids for multi-dimensions. Recent studies have shown that
replacing the polynomial by radial basis functions in pseudospectral method
(RBF-PS) has the advantage of using irregular grids for multivariate systems. A
RBF-PS algorithm has been presented here for the numerical solution of
inhomogeneous Helmholtz's equation using Gaussian RBF for derivative
approximation. Efficacy of RBF approximated derivatives has been checked
through error analysis comparison with PS method. Comparative study of PS,
RBF-PS and finite difference approach for the solution of a linear boundary
value problem has been performed. Finally, a typical frequency domain acoustic
wave propagation problem has been solved using Dirichlet boundary condition and
a point source. The algorithm presented here can be extended further for
seismic modeling with complexities associated with absorbing boundary
conditions.
