HOMOGENEOUS DIFFERENCE SCHEMES FOR ONE-DIMENSIONAL PROBLEMS WITH GENERALIZED SOLUTIONS

Exact and truncated homogeneous difference schemes of arbitrary order of accuracy are constructed and investigated for the one-dimensional second-order equation, with generalized solutions in We Mathematical tools are developed for studying the accuracy of truncated difference schemes. It is assumed that k(x) is a measurable function, while q(x) and (i) are generalized derivatives of functions in the class this allows one to include the case in which 5(1) and f(x) are -functions. It is shown that truncated schemes of mth order have accuracy, where h is the mesh step size and a number depending on the exponents ?, f, pq, and Pf. In the case of piecewise smooth coefficients n = 0, and the estimates obtained coincide with results of the theory of homogeneous difference schemes of Tikhonov and Samarskii. 1988 IOP Publishing Ltd.

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