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Methods > Ordinary Differential Equations

Methods for Solving Ordinary Differential Equations

Exact and Analytical Methods

• Estevez, P. G., Kuru, S., Negro, J., and Nieto, L. M., Factorization of a class of almost linear second order differential equations, J. Phys. A: Math. Theor., Vol. 40, pp. 9819–9824, 2007.
• Chow, C.C., Multiple scale analysis, From Scholarpedia, 2007.
• Sanders, J.A., Averaging, From Scholarpedia, 2006.
• Khorasani, S. and Adibi, A., Analytical solution of linear ordinary differential equations by differential transfer matrix method, Electronic J. Differential Equations, No 79, pp. 1-18, 2003.
• Kudryashov, N.A., Simplest equation method to look for exact solutions of nonlinear differential equations, Chaos, Solitons and Fractals, Vol. 24, pp. 1217-1231, 2005.
• Zaitsev, V.F., On new directions of group analysis of ordinary differential equations, In: Problems of Nonlinear Analysis in Engineering Systems, Kazan, Vol. 8, No. 1 (15), pp. 12-23, 2002.
• Encyclopedia of dynamical systems, From Scholarpedia

Numerical Methods

• Butcher, J., Runge-Kutta methods, From Scholarpedia, 2007.
• Jackiewicz, Z., General linear methods, From Scholarpedia, 2007.
• Auzinger, W., Karner, E., Koch, O., and Weinmuller, E., Collocation methods for the solution of eigenvalue problems for singular ordinary differential equations, 2006.
• Butcher, J.C., Jackiewicz, Z., and Wright, W.M., Error propagation of general linear methods for ordinary differential equations, 2006.
• Niesen, J., On the global error of discretization methods for ordinary differential equations, 2004.