On the estimate the L<sub>2</sub> and L<sub>∞</sub> norm of the error for the initial value problems


Our objective in this paper is to examine conditions under which the variational principle has a global extremal properties and to complete the error estimate procedure of [5].We will use the value of the functional to estimate the L<sub>2</sub> and L_∈fty norm of the error for the initial value problems, described by a non-linear second order differential equation belonging to the class treated in [5]. In our analysis integral inequalities given in [1-4] are of central importance.The analysis will be illustrated by an concrete example.

DOI Code: 10.1285/i15900932v15n1p121

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