A New Numerical Technique for Solving Volterra Integral Equations Using Chebyshev Spectral Method
Ahmed A. Khidir
Abstract
In this work, we propose a new method for solving Volterra integral equations. The technique is based on the Chebyshev spectral collocation method. The application of the proposed method leads Volterra integral equation to a system of algebraic equations that are easy to solve. Some examples are presented and compared with some methods in the literature to illustrate the ability of this technique. The results demonstrate that the new method is more efficient, convergent, and accurate to the exact solution.
Topics & Concepts
Volterra integral equationChebyshev filterIntegral equationAlgebraic equationMathematicsCollocation methodChebyshev polynomialsSpectral methodCollocation (remote sensing)Applied mathematicsChebyshev nodesChebyshev iterationVolterra equationsMathematical analysisComputer scienceNonlinear systemDifferential equationPhysicsOrdinary differential equationMachine learningQuantum mechanicsFractional Differential Equations SolutionsIterative Methods for Nonlinear EquationsMathematical functions and polynomials