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<p>In this manuscript, an efficient numerical algorithm based on semi-orthogonal B-spline wavelets and quasi-linearization approximation is designed to investigate the behavior of viscous Burgers’ and coupled Burgers’ model. These models find significant application in complicated mathematical modeling such as fluid dynamics, cell population dynamics, pollutant dispersion and sediment transport, etc. In this combined approach, forward finite difference method is utilize to discretize the time derivative and then quasi-linearization process is applied to address the non-linearity. While, spatial discretization is performed by using semi-orthogonal B-spline wavelets. A rigorous analysis confirms the unconditional stability of the semi-discrete model, subsequently the proof of convergence analysis is examined in <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathcal {L}^2\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="script">L</mi> </mrow> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation> and <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(H_0^1\)</EquationSource> <EquationSource Format="MATHML"><math> <msubsup> <mi>H</mi> <mn>0</mn> <mn>1</mn> </msubsup> </math></EquationSource> </InlineEquation> spaces. Finally, the investigation demonstrates how computational modeling effectively handles cases of small kinematic viscosity coefficients (<InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(10^{-5}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>5</mn> </mrow> </msup> </math></EquationSource> </InlineEquation>) and limited mesh points, where traditional methods prove inadequate. The results and findings of designed algorithm is demonstrated via Tables and Figures.</p>

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An efficient B-spline wavelet algorithm for simulation of viscous Burgers’ and coupled Burgers’ equations

  • 期刊论文

  • 发表日期：

    2025年10月15日

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  • Deepak Kumar,
  • Sapna Pandit

摘要

In this manuscript, an efficient numerical algorithm based on semi-orthogonal B-spline wavelets and quasi-linearization approximation is designed to investigate the behavior of viscous Burgers’ and coupled Burgers’ model. These models find significant application in complicated mathematical modeling such as fluid dynamics, cell population dynamics, pollutant dispersion and sediment transport, etc. In this combined approach, forward finite difference method is utilize to discretize the time derivative and then quasi-linearization process is applied to address the non-linearity. While, spatial discretization is performed by using semi-orthogonal B-spline wavelets. A rigorous analysis confirms the unconditional stability of the semi-discrete model, subsequently the proof of convergence analysis is examined in \(\mathcal {L}^2\) L 2 and \(H_0^1\) H 0 1 spaces. Finally, the investigation demonstrates how computational modeling effectively handles cases of small kinematic viscosity coefficients ( \(10^{-5}\) 10 - 5 ) and limited mesh points, where traditional methods prove inadequate. The results and findings of designed algorithm is demonstrated via Tables and Figures.