One of the simplest schemes of the degenerate matrix method with nodes as zeroes of Chebyshev polynomials of the second kind is considered. Performance of simple iterations and some modifications of Newton method for the discrete problem is compared.
Santrauka. Šiame darbe toliau nagrinėjamas išsigimusių matricų metodas netiesinių diferencialinių lygčių pradinio uždavinio sprendimui. Sudarant metodo algoritmą naudojami antrojo tipo Cebyševo polinomų nuliai bei specialiai parenkamos konstantos aproksimuojant išvestinės kvaziatvirkštinę matricą. Metodas pritaikomas dviejų tipų iteraciniams algoritmams: paprastųjų iteracijų ir Niutono metodams. Pateikiami skaitinio eksperimento rezultatai ir naujasis metodas palygintas su populiariaisiais skaitiniais algoritmais.
Cirulis, T., & Lietuvietis, O. (1999). Degenerate matrix method with Chebyshev nodes for solving nonlinear systems of differential equations. Mathematical Modelling and Analysis, 4(1), 51-57. https://doi.org/10.3846/13926292.1999.9637110
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