The Operator Approach to Problems of Stability and Convergence of Solutions of Difference Equations and the Convergence of Various Iteration ProceduresScripta Mathematica, Yeshiva University, 1957 - 104 頁 |
內容
Stability Analysis for Other Difference Schemes for | 13 |
Convergence of Various Iteration Procedures | 22 |
Stability Analysis of Various Difference Schemes | 31 |
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absolute values Accordingly alternative analysis Appendix applied appropriate approximation arbitrary Assume becomes boundary conditions bounded clear coefficients components conclusion Consider consideration convergence corresponding cos2 counterpart defined denote determinantal equation determine difference analog difference equation difference scheme differential equation discussed easily eigenvalues eigenvectors elements equal equations derived error expression Finally follows given identical implicit difference iteration procedure known largest last equation last inequality leads manner matrix method necessary negative numerically smaller obtain once operator present principal diagonal problem proof prove readily seen region relation remains replaced respectively roots satisfy shown similar Similarly sin² smaller than unity solution stability successive tends theorem tion true Uk+1 ultimately Un+1 upperbound Ux+1 vector whence written yields λε Υπ