Trigonometric <i>B</i>-spline based <i>ε</i>-uniform scheme for singularly perturbed problems with Robin boundary conditions

Singh, Satpal; Kumar, Devendra; Deswal, Komal

doi:10.1080/10236198.2022.2099273

Cited by 7 publications

(1 citation statement)

References 40 publications

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“…Yaseen et al, [13] numerically solved the generalized form of time-fractional diffusion equation using cubic trigonometric B-splines with collocation method but having trigonometric spline basis makes the subsequent process very difficult as the matrix system generated by this method is relatively very large. This type of PDE is also studied by Singh et al, [14] in the form of reaction-diffusion equation using trigonometric Bspline with Neumann and Dirichlet boundary conditions. Jena and Senapati [15] presented solution of heat and advection-diffusion equation using improvised cubic B-spline collocation, finite element method and Crank-Nicolson technique but these methods have high arithmetic computations, lower accuracy, and complexity in computer programming.…”

Section: Introductionmentioning

confidence: 95%

Numerical Solution of Heat Equation using Modified Cubic B-spline Collocation Method

Mudassar Iqbal,

Nooraini Zainuddin,

Hanita Daud

et al. 2024

ARNHT

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In this paper, a collocation method is presented based on the Modified Cubic B-spline Method (MCBSM) for the numerical solution of the heat equation. The PDE is fully discretized by using the Modified Cubic B-spline basis collocation for spatial discretization and the finite difference method is used for the time discretization. A numerical example from PDE is used to evaluate the accuracy of the proposed method. The numerical results are evaluated in comparison to the exact solutions. The findings consistently indicate that the suggested technique provides good error estimates. We also discovered that our proposed method was unconditionally stable. Hence, based on the results and the efficiency of the method, the method is suitable for solving heat equation.

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Section: Introductionmentioning

confidence: 95%