Application of sextic B-spline collocation method for solving inverse the modified Kawahara equation

Torabi, Fateme; Pourgholi, Reza

doi:10.1007/s13226-022-00283-0

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2024

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“…The implicit Crank -Nicolson method can be used to efficiently solve the heat equation [19,20]. Many authors [21][22][23][24][25] have used higher order B-splines such as quintic, quartic, sextet and septic B-splines for the solutions of different PDEs but faced computational higher cost. Also, Riccati matrix delay differential equations has solved with variational iteration method in these papers [26][27][28][29][30].…”

Section: Introductionmentioning

confidence: 99%

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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