Mixed problems for separate variable coefficient wave equations: The non-Dirichlet case. Continuous numerical solutions with a priori error bounds
This paper deals with the construction of continuous numerical solutions of non-Dirichlet mixed wave systems of the form u(tt) = (b(t))(a(x))u(xx), 0   0, a(1)u(0, t) + a(2)u(x)(0, t) = 0, b(1)u(L, t) + b(2)u(x)(L, t) = 0, u(x, 0) = f(x), u(t)(x, 0) = g(x), 0 less than or equal to x less than or equal to L. Uniqueness and existence of an exact series solution are studied. Given an admissible error a > 0 and a bounded domain D(T) = [0, L] x [0, T], T > 0, an approximate continuous numerical solution involving only a finite number of eigenvalues and eigenfunctions is given so that the error with respect to the exact solution is less than a uniformly in D(T). The admissible error for the finite number of approximated eigenvalues, eigenfunctions, and Sturm-Liouville coefficients is determined in order to grantee the required accuracy. (C) 1999 Elsevier Science Ltd. All rights reserved.
mixed problem separate variable coefficient wave equation a priori error bound non-dirichlet condition