Abstract
Using an idea due toCourant, Isaacson andRees, Törnig andZiegler showed convergence of difference approximations to initial-value problems with first-order systems of quasilinear hyperbolic differential equations in two independent variables by constructing an ordinary difference or differential equation, which has a solution being a majorant of the error and decreasing for decreasing step-sizes. Here this method is generalized to a wider class of quasilinear problems (not necessary hyperbolic, not necessary of first order, not necessary in only two independent variables).
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Literatur
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Ansorge, R. Konvergenz von Differenzenverfahren für quasilineare Anfangswertaufgaben. Numer. Math. 13, 217–225 (1969). https://doi.org/10.1007/BF02167552
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DOI: https://doi.org/10.1007/BF02167552