Solving two-dimensional nonlinear fuzzy Volterra integral equations by homotopy analysis method
Atanaska Georgieva
Abstract
Abstract The purpose of the paper is to find an approximate solution of the two-dimensional nonlinear fuzzy Volterra integral equation, as homotopy analysis method (HAM) is applied. Studied equation is converted to a nonlinear system of Volterra integral equations in a crisp case. Using HAM we find approximate solution of this system and hence obtain an approximation for the fuzzy solution of the nonlinear fuzzy Volterra integral equation. The convergence of the proposed method is proved. An error estimate between the exact and the approximate solution is found. The validity and applicability of the HAM are illustrated by a numerical example.
Topics & Concepts
MathematicsHomotopy analysis methodVolterra integral equationIntegral equationNonlinear systemFuzzy logicConvergence (economics)HomotopyApplied mathematicsMathematical analysisVolterra equationsPure mathematicsComputer scienceEconomic growthPhysicsArtificial intelligenceQuantum mechanicsEconomicsFuzzy Systems and OptimizationFractional Differential Equations SolutionsFunctional Equations Stability Results