Haar wavelet operational matrix of fractional order integration and its applications in solving the fractional order differential equations

A numerical method for solving boundary value problems for fractional differential equations

New algorithms for the numerical solution of nonlinear Fredholm and Volterra integral equations using Haar wavelets

A new Bernoulli matrix method for solving high-order linear and nonlinear Fredholm integro-differential equations with piecewise intervals

A quadrature rule based on uniform Haar wavelets and hybrid functions is proposed to find approximate values of definite integrals. The wavelet-based algorithm can be easily extended to find numerical approximations for double, triple and improper integrals. The main advantage of this method is its efficiency and simple applicability. Error estimates of the proposed method alongside numerical examples are given to test the convergence and accuracy of the method.

A comparative study of numerical integration based on Haar wavelets and hybrid functions

Numerical solution of nonlinear Fredholm integral equations of the second kind using Haar wavelets

In this work, we present a computational method for solving Volterra integral equations of the second kind with weakly singular kernel which is based on the use of Haar wavelets and properties of Block-PulseFunctions(BPF). Error analysis is worked out that shows efficiency and the order of convergence of the method. Finally, we also give some numerical examples.

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Haar Wavelet Method to Solve Volterra Integral Equations with Weakly Singular Kernel by Collocation Method

A numerical method for solving nonlinear Fredholm-Volterra integral equations is presented. The method is based upon Lagrange functions approximations. These functions together with the Gaussian quadrature rule are then utilized to reduce the Fredholm-Volterra integral equations to the solution of algebraic equations. Some examples are included to demonstrate the validity and applicability of the technique.

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Lagrange Functions Method for Solving Nonlinear Hammerstein Fredholm-Volterra Integral Equations

A numerical method for solving nonlinear Fredholm integro differential equations of the second kind is presented. The method is based upon Lagrange functions approximation. Quadrature rule and collocation points are utilized to reduce the main problem to nonlinear system of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique.

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Application of Lagrange Interpolation for Nonlinear Integro Differential Equations

In this work, we present a computational method for solving nonlinear Fredholm-Volterra integral equations of the second kind which is based on replacement of the unknown function by truncated series of well known Block-Pulse functions (BPfs) expansion. Error analysis is worked out that shows efficiency of the method. Finally, we also give some numerical examples.

/pdf/numerical-solution-of-nonlinear-fredholm-volterra-integtral-13ffn6vdz2.pdf

Ahmad Shahsavaran

Papers

Numerical solution of nonlinear Fredholm integral equations of the second kind using Haar wavelets

Haar Wavelet Method to Solve Volterra Integral Equations with Weakly Singular Kernel by Collocation Method

Lagrange Functions Method for Solving Nonlinear Hammerstein Fredholm-Volterra Integral Equations

Application of Lagrange Interpolation for Nonlinear Integro Differential Equations

Numerical Solution of Nonlinear Fredholm-Volterra Integtral Equations via Piecewise Constant Function by Collocation Method