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A robust framework for solving PDEs: Biorthogonal spline wavelet methods Cover

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A robust framework for solving PDEs: Biorthogonal spline wavelet methods

International Journal of Mathematics and Computer in Engineering

Volume 4 (2026): Issue 1 (June 2026)

By: Mutaz Mohammad and Alexander Trounev

Open Access

|May 2026

Figures & tables

Figures & Tables

Biorthogonal spline scaling and wavelet functions of order 2 and dual order 4, and of order 3 and dual order 5.

Graphs of the exact solution, numerical solution at different time steps, and comparison between the exact and numerical solutions for n = 2 and M = 8.

Graphs of the numerical solution at different time steps and the error bound for n = 2 and M = 8.

Graphs of the numerical solution at different time steps, and comparison between the exact and numerical solutions for n = 3 and M = 16.

Graphs of the numerical solution at different time steps, and the error bound for n = 3 and M = 16.

Convergence rate graphs of the numerical solutions for the Haar and BSW-2 wavelet methods, respectively.

Log-log plots of numerical solutions for Haar and BSW-2 wavelet methods, respectively.

Numerical values for xl, t and corresponding u[xl,t] for two methods_

t=0	t=0	t=0	t=0.3	t=0.3	t=0.6	t=0.6	t=0.9	t=0.9
x_l	BSW-2	Haar	BSW-2	Haar	BSW-2	Haar	BSW-2	Haar
116\frac1{16}	0	0	0.1867561	0.1850020	0.2158150	0.2140760	0.0752277	0.0745150
316\frac3{16}	0	0	0.1451483	0.1440110	0.1705720	0.1695220	0.0548761	0.0542550
516\frac5{16}	0	0	0.1130518	0.1120270	0.1330290	0.1320680	0.0434034	0.0430950
716\frac7{16}	0	0	0.0883459	0.0875280	0.1037956	0.1030230	0.0336308	0.0332450
916\frac9{16}	0	0	0.0688853	0.0682610	0.0810188	0.0803560	0.0263730	0.0261660
1116\frac11{16}	0	0	0.0537768	0.0532920	0.0632059	0.0627320	0.0205080	0.0203022
1316\frac13{16}	0	0	0.0419592	0.0415060	0.0493254	0.0488210	0.0160445	0.0159001
1516\frac15{16}	0	0	0.0327424	0.0324060	0.0384910	0.0381090	0.0124974	0.0124034

Articles in this issue

DOI: https://doi.org/10.2478/ijmce-2026-0005 | Journal eISSN: 2956-7068

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Language: English

Page range: 65 - 76

Submitted on: Oct 7, 2024

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Accepted on: Feb 14, 2025

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Published on: May 27, 2026

Published by: Harran University

In partnership with: Paradigm Publishing Services

Publication frequency: 2 issues per year

Keywords:

biorthogonal spline wavelets,

Diffusion equation,

collocation methods,

boundary conditions

Related subjects:

Computer sciences,

Computer sciences, other,

Introductions and overviews,

Engineering, other,

General mathematics,

© 2026 Mutaz Mohammad, Alexander Trounev, published by Harran University
This work is licensed under the Creative Commons Attribution 4.0 License.

Volume 4 (2026): Issue 1 (June 2026)

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