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The element of pesedospectral-multiwavelet-Galerkin method, and how to combine it with penalty method for treating boundary conditions are given.Multiwavelet bases don’t overlap on the given scale, and possess the same compact set in a group of several functions, so they can be directly used to the numerical discretion on the finite interval.Numerical tests show that general boundary conditions can be enforced with the penalty method, and that pesedospectral-multiwavelet-Galerkin method can well track the solutions’ development.This also proves that pesedospectral-multiwavelet-Galerkin method is effective.