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Title

SOME POINTS ON THE RECENTLY APPROACHES FOR NON-LINEAR FUNCTIONAL EQUATIONS

Writers

BIAZAR JAFAR | AYATI ZAINAB

Pages

 Start Page | End Page

Abstract

 NON-LINEAR FUNCTIONAL EQUATIONS, FUNCTIONAL EQUATIONS USUALLY APPEAR IN MATHEMATICAL MODELLING. OF MANY REAL WORLD PROBLEMS. THESE EQUATIONS ARE MORE INTERESTING FOR MATHEMATICIANS AND ENGINEERS. APPLICATION OF CLASSICAL ANALYTICAL METHODS, ARE VERY RESTRICTED. LINEARIZATION OR DISCRETIZATION HAVE BEEN USED BY MANY RESEARCHERS WHEN DEALING WITH NON-LINEAR FUNCTIONAL EQUATION. THESE APPROACHES CAUSE LOOSING SOME OF THE REAL WORLD RE-ALITY, AND THE RESULTS ARE NOT USUALLY IN GOOD AGREEMENTS WITH AN EXACT SOLUTION. NOWADAYS, MANY APPROACHES REFERRED TO AS, SEMI NUMERICAL, OR SEMI ANALYTICAL ARE USED TO SOLVE SUCH EQUATIONS. THESE METHODS USUALLY LEADS TO AN APPROXIMATION TO AN AN-ALYTIC SOLUTION OF THE EQUATION UNDER STUDY. IN THIS TALK, SOME OF THESE METHODS, WHICH ARE MORE KNOWN, ARE ADDRESSED AND ARE COMPARED. SOME OF NEW APPROACHES FOR SOLVING NON-LINEAR PROBLEMS ARE, ADM: ADOMIAN DECOMPOSITION METHOD, HAM: HOMOTOPY ANALYSIS METHOD, HPM: HOMOTOPY PERTURBATION METHOD. L-EXPANSION, G′/G- EXPANSION, TRIGONOMETRIC: SIN-COS, TAN, TANH-COTH, METHODS. EXP FUNCTION, AND VARIATION ITERATION METHOD.

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