Error Estimates for Finite Difference Methods for a Wide-angle ‘parabolic’ Equation
نویسندگان
چکیده
We consider a model initialand boundary-value problem for a third-order p.d.e., a wide-angle ‘parabolic’ equation frequently used in underwater acoustics, with depthand rangedependent coefficients in the presence of horizontal interfaces and dissipation. After commenting on the existence–uniqueness theory of solution of the equation, we discretize the problem by a secondorder finite difference method of Crank–Nicolson type for which we prove stability and optimal-order error estimates in suitable discrete L, H and maximum norms. We also prove, under certain conditions, that the forward Euler scheme is also stable and convergent for the problem at hand.
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