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A note on rapid convergence of approximate solutions for second order periodic boundary value problems

Rahmat A. Khan, Bashir Ahmad (2005)

Archivum Mathematicum

In this paper, we develop a generalized quasilinearization technique for a nonlinear second order periodic boundary value problem and obtain a sequence of approximate solutions converging uniformly and quadratically to a solution of the problem. Then we improve the convergence of the sequence of approximate solutions by establishing the convergence of order k ( ...

An extension of the method of quasilinearization

Tadeusz Jankowski (2003)

Archivum Mathematicum

The method of quasilinearization is a well–known technique for obtaining approximate solutions of nonlinear differential equations. This method has recently been generalized and extended using less restrictive assumptions so as to apply to a larger class of differential equations. In this paper, we use this technique to nonlinear differential problems.

Approximate solution of an inhomogeneous abstract differential equation

Emil Vitásek (2012)

Applications of Mathematics

Recently, we have developed the necessary and sufficient conditions under which a rational function F ( h A ) approximates the semigroup of operators exp ( t A ) generated by an infinitesimal operator A . The present paper extends these results to an inhomogeneous equation u ' ( t ) = A u ( t ) + f ( t ) .

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