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A high order wavelet integral collocation method (WICM) is developed forgeneral nonlinear boundary value problems in physics. This method isestablished based on Coiflet approximation of multiple integrals of intervalbounded functions combined with an accurate and adjustable boundary extensiontechnique. The convergence order of this approximation has been proven to be Nas long as the Coiflet with N-1 vanishing moment is adopted, which can be anypositive even integers. Before the conventional collocation method is appliedto the general problems, the original differential equation is changed into itsequivalent form by denoting derivatives of the unknown function as newfunctions and constructing relations between the low and high orderderivatives. For the linear cases, error analysis has proven that the proposedWICM is order N, and condition numbers of relevant matrices are almostindependent of the number of collocation points. Numerical examples of a widerange of nonlinear differential equations in physics demonstrate that accuracyof the proposed WICM is even greater than N, and most interestingly, suchaccuracy is independent of the order of the differential equation to be solved.Comparison to existing numerical methods further justifies the accuracy andefficiency of the proposed method.

A wavelet integral collocation method for nonlinear boundary value problems in Physics