A new least‐squares‐based reproducing kernel method for solving regular and weakly singular Volterra‐Fredholm integral equations with smooth and nonsmooth solutions
Minqiang Xu, Jing Niu, Emran Tohidi, Jinjiao Hou, Danhua Jiang
Abstract
Based on the least‐squares method, we proposed a new algorithm to obtain the solution of the second kind of regular and weakly singular Volterra‐Fredholm integral equations in reproducing kernel spaces. The stability and uniform convergence of the algorithm are investigated in detail. Numerical experiments verify the theoretical findings. Meanwhile, this method is also applicable to the nonlinear Volterra integral equations. Test problems which have non‐smooth solutions are also considered, and our proposed method is efficient as some recent Krylov subspace methods such as LSQR and LSMR.
Topics & Concepts
MathematicsKernel (algebra)Integral equationFredholm integral equationVolterra integral equationConvergence (economics)Nonlinear systemApplied mathematicsStability (learning theory)Krylov subspaceMathematical analysisLinear systemPure mathematicsComputer scienceMachine learningPhysicsEconomic growthQuantum mechanicsEconomicsFractional Differential Equations SolutionsNumerical methods in engineeringIterative Methods for Nonlinear Equations