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This paper is concerned with the construction and analysis ofcompact finite difference approximations to the model linearsource problem (pu')' + qu = f where the functions p,q, and f can have jump discontinuities at a finite number ofpoints. Explicit formulae that give O(h2) O(h3) and O(h4) accuracyare derived, and a procedure for computing three-point schemesof any prescribed order of accuracy is presented. A rigoroustruncation and discretization error analysis is offered. Numericalresults are also given. 相似文献
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