Solving parabolic differential equations via Haar wavelets: A focus on integral boundary conditions

Abstract

The article addresses the solution of parabolic differential equations with integral boundary conditions using the Haar wavelet collocation method. This approach employs a linear combination of Haar wavelet functions to estimate the largest derivatives in the governing equation. The integral boundary conditions are incorporated by repeatedly integrating the highest derivative to formulate equations for the unknowns. Haar wavelets are particularly suitable for approximating solutions to differential equations due to their compact support and multiresolution properties. Numerical experiments on various test cases show that the proposed method yields accurate results, especially when the parameters of the integral boundary conditions are negative.

Keywords

Haar wavelets collocation method / Integral boundary conditions / Parabolic differential equations / Numerical analysis

Funding

None.

Declaration of competing interest

The authors declare there is no competing interest regarding this work.

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