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LINEAR APPROXIMATION AND ASYMPTOTIC EXPANSION ASSOCIATED WITH THE SYSTEM OF NONLINEAR FUNCTIONAL EQUATIONS

  • 31/03/2022
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THIS PAPER IS DEVOTED TO THE STUDY OF THE FOLLOWING PERTURBED SYSTEM OF NONLINEAR FUNCTIONAL EQUATIONS EQUATION PRESENTED WHERE IS A SMALL PARAMETER, AIJK, BIJK ARE THE GIVEN REAL CONSTANTS, R IJK, SIJK, XIJK: , G I : R, : R2 R ARE THE GIVEN CONTINUOUS FUNCTIONS AND FI : R ARE UNKNOWN FUNCTIONS. FIRST, BY USING THE BANACH FIXED POINT THEOREM, WE FIND SUFFICIENT CONDITIONS FOR THE UNIQUE EXISTENCE AND STABILITY OF A SOLUTION OF (E). NEXT, IN THE CASE OF C2(R 2;R), WE INVESTIGATE THE QUADRATIC CONVERGENCE OF (E). FINALLY, IN THE CASE OF CN(R2,R) AND SUFFICIENTLY SMALL, WE ESTABLISH AN ASYMPTOTIC EXPANSION OF THE SOLUTION OF (E) UP TO ORDER N + 1 IN . IN ORDER TO ILLUSTRATE THE RESULTS OBTAINED, SOME EXAMPLES ARE ALSO GIVEN. COPYRIGHT BY FACULTY OF MATHEMATICS AND INFORMATION SCIENCE, WARSAW UNIVERSITY OF TECHNOLOGY.

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