Open AccessNumerical and analytic method for solvingproposal New Type for fuzzy nonlinear volterra integral equation
Author(s) -
Sameer Qasim Hasan,
Alan Abdulqader jalal
Publication year - 2016
Publication title -
journal of advances in mathematics
Language(s) - English
Resource type - Journals
ISSN - 2347-1921
DOI - 10.24297/jam.v12i5.4009
Subject(s) - mathematics , volterra integral equation , homotopy analysis method , integral equation , nonlinear system , homotopy , mathematical analysis , kernel (algebra) , fuzzy logic , uniqueness , type (biology) , summation equation , discrete mathematics , pure mathematics , ecology , physics , quantum mechanics , biology , linguistics , philosophy
In this paper, we proved the existence and uniqueness and convergence of the solution of new type for nonlinear fuzzy volterra integral equation . The homotopy analysis method are proposed to solve the new type fuzzy nonlinear Volterra integral equation . We convert a fuzzy volterra integral equation for new type of kernel for integral equation, to a system of crisp function nonlinear volterra integral equation . We use the homotopy analysis method to find the approximate solution of the system and hence obtain an approximation for fuzzy solution of the nonlinear fuzzy volterra integral equation . Some numerical examples is given and results reveal that homotopy analysis method is very effective and compared with the exact solution and calculate the absolute error between the exact and AHM .Finally using the MAPLE program to solve our problem .