Abstract
An initial value problem for stiff systems of first-order ordinary differential equations is considered. In the class of (m, k)-methods, two integration algorithms with a variable step size based on second (m = k = 2) and third (k = 2, m = 3) order-accurate schemes are constructed in which both analytical and numerical Jacobian matrices can be frozen. A theorem on the maximum order of accuracy of (m, 2)-methods with a certain approximation of the Jacobian matrix is proved. Numerical results are presented.
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Original Russian Text © E.A. Novikov, 2011, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2011, Vol. 51, No. 12, pp. 2194–2208.
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Novikov, E.A. Approximation of the Jacobian matrix in (m, 2)-methods for solving stiff problems. Comput. Math. and Math. Phys. 51, 2065–2078 (2011). https://doi.org/10.1134/S0965542511120153
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DOI: https://doi.org/10.1134/S0965542511120153