Solving Nonlinear Boundary Value Problems Using the Higher Order Haar Wavelet Method
Mart Ratas, Jüri Majak, Andrus Salupere
Abstract
The current study is focused on development and adaption of the higher order Haar wavelet method for solving nonlinear ordinary differential equations. The proposed approach is implemented on two sample problems—the Riccati and the Liénard equations. The convergence and accuracy of the proposed higher order Haar wavelet method are compared with the widely used Haar wavelet method. The comparison of numerical results with exact solutions is performed. The complexity issues of the higher order Haar wavelet method are discussed.
Topics & Concepts
Haar waveletWaveletHaarMathematicsApplied mathematicsNonlinear systemBoundary value problemCascade algorithmDiscrete wavelet transformConvergence (economics)Mathematical analysisWavelet transformComputer scienceArtificial intelligencePhysicsEconomicsQuantum mechanicsEconomic growthFractional Differential Equations SolutionsIterative Methods for Nonlinear EquationsDifferential Equations and Numerical Methods