Exponential spline for the numerical solutions of linear Fredholm integro-differential equations
Taherh Tahernezhad, R. Jalilian
Abstract
Abstract In this paper, we introduce a new scheme based on the exponential spline function for solving linear second-order Fredholm integro-differential equations. Our approach consists of reducing the problem to a set of linear equations. We prove the convergence analysis of the method applied to the solution of integro-differential equations. The method is described and illustrated with numerical examples. The results reveal that the method is accurate and easy to apply. Moreover, results are compared with the method in (J. Comput. Appl. Math. 290:633–640, 2015).
Topics & Concepts
MathematicsFredholm integral equationExponential integratorSpline (mechanical)Ordinary differential equationMathematical analysisNumerical partial differential equationsApplied mathematicsExponential functionPartial differential equationDifferential equationIntegral equationDifferential algebraic equationStructural engineeringEngineeringFractional Differential Equations SolutionsDifferential Equations and Numerical MethodsNumerical methods for differential equations