A Chebyshev Wavelet Collocation Method for Some Types of Differential Problems
Sharanjeet Dhawan, J. A. Tenreiro Machado, Dariusz W. Brzeziński, M.S. Osman
Abstract
In the past decade, various types of wavelet-based algorithms were proposed, leading to a key tool in the solution of a number of numerical problems. This work adopts the Chebyshev wavelets for the numerical solution of several models. A Chebyshev operational matrix is developed, for selected collocation points, using the fundamental properties. Moreover, the convergence of the expansion coefficients and an upper estimate for the truncation error are included. The obtained results for several case studies illustrate the accuracy and reliability of the proposed approach.
Topics & Concepts
WaveletChebyshev filterApplied mathematicsTruncation errorCollocation (remote sensing)Chebyshev equationMathematicsConvergence (economics)Collocation methodChebyshev iterationMatrix (chemical analysis)Chebyshev nodesChebyshev polynomialsTruncation (statistics)Mathematical optimizationComputer scienceMathematical analysisDifferential equationOrthogonal polynomialsOrdinary differential equationStatisticsMachine learningClassical orthogonal polynomialsComposite materialMaterials scienceEconomic growthEconomicsArtificial intelligenceFractional Differential Equations SolutionsImage and Signal Denoising MethodsDifferential Equations and Numerical Methods