Finite Difference Discretization with Variable Mesh of the Schrödinger Equation in a Variable Domain
نویسندگان
چکیده
Abstract. We consider a partial differential equation of Schrödinger type, known as the ‘parabolic’ approximation to the Helmholtz equation in the theory of sound propagation in an underwater, rangeand depth-dependent environment with a variable bottom. We solve an associated initialand boundary-value problem by a finite difference scheme of Crank-Nicolson type on a variable mesh. We prove that the method is stable in l2, establish optimal, second-order error estimates and show results of relevant numerical experiments.
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