The Haar wavelets based numerical solution of Reccati equation with integral boundary condition
Muhammad Ahsan, Amir Khan, Seza Dinibütün, Imtiaz Ahmad, Hijaz Ahmad, Nantapat Jarasthitikulchai, Weerawat Sudsutad
Abstract
A Haar wavelet collocation method (HWCM) is presented for the solution of Riccati equation subject to the two-point and integral boundary condition. The qua?silinearization technique is applied to linearized the Riccati equation and then the linearized equation with boundary condition is solved by converting into system of algebraic equation with the help of Haar wavelets. We have considered three different form of Reccati equation, two having integral boundary condition and one with two-point boundary condition. The numerical results obtained by HWCM are stable, efficient and convergent.
Topics & Concepts
Riccati equationMathematicsMathematical analysisBoundary value problemAlgebraic Riccati equationHaar waveletAlgebraic equationIntegral equationRobin boundary conditionMixed boundary conditionCollocation methodBoundary (topology)WaveletPartial differential equationDifferential equationWavelet transformPhysicsDiscrete wavelet transformOrdinary differential equationComputer scienceNonlinear systemQuantum mechanicsArtificial intelligenceFractional Differential Equations SolutionsNumerical methods in engineeringElectromagnetic Scattering and Analysis