Approximate Solutions by Truncated Taylor Series Expansions of Nonlinear Differential Equations and Related Shadowing Property with Applications
De la Sen Parte, Manuel
Ibeas Hernández, Asier
Nistal Riobello, Raúl
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Abstract and Applied Analysis 2014 : (2014) // Article ID 956318
This paper investigates the errors of the solutions as well as the shadowing property of a class of nonlinear differential equations which possess unique solutions on a certain interval for any admissible initial condition. The class of differential equations is assumed to be approximated by well-posed truncated Taylor series expansions up to a certain order obtained about certain, in general nonperiodic, sampling points t(i) is an element of [t(0), t(J)] for i = 0, 1, . . . , J of the solution. Two examples are provided.