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<p>The manuscript considers the fractional-order Burger’s equation in two dimensions, which is a non-linear viscous fluid dynamical model. A systematic numerical technique involving a finite difference-based L1-scheme is implemented to approximate the solution of the proposed problem. The proposed technique involves the semi-discretisation of the fractional-order time derivative using the L1-scheme, followed by orthogonal collocation using Hermite splines. This technique fully discretises the 2D Burger’s equation for both the time and spatial domains into an algebraic system of equations. To ensure the accuracy and reliability of the method, numerical illustrations are presented for validation. The unconditional stability and optimal order of convergence of the technique signify its applicability to higher-order non-linear boundary value problems. The work is further supported by the comparison of the numerical values obtained from the proposed technique with those already reported in the literature.</p>

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Computationally efficient numerical technique to study 2D time fractional Burger’s equation

  • 期刊论文

  • 发表日期：

    2026年3月25日

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  • Priyanka,
  • Saroj Sahani,
  • Fateh Mebarek-Oudina,
  • Shelly Arora

摘要

The manuscript considers the fractional-order Burger’s equation in two dimensions, which is a non-linear viscous fluid dynamical model. A systematic numerical technique involving a finite difference-based L1-scheme is implemented to approximate the solution of the proposed problem. The proposed technique involves the semi-discretisation of the fractional-order time derivative using the L1-scheme, followed by orthogonal collocation using Hermite splines. This technique fully discretises the 2D Burger’s equation for both the time and spatial domains into an algebraic system of equations. To ensure the accuracy and reliability of the method, numerical illustrations are presented for validation. The unconditional stability and optimal order of convergence of the technique signify its applicability to higher-order non-linear boundary value problems. The work is further supported by the comparison of the numerical values obtained from the proposed technique with those already reported in the literature.