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Singh, Swarn, Bhatt, Sandeep, Singh, Suruchi. (1400). Cubic B-spline collocation method on a non-uniform mesh for solving nonlinear parabolic partial differential equation. سامانه مدیریت نشریات علمی, 10(1), 28-43. doi: 10.22034/cmde.2020.39472.1726
Swarn Singh; Sandeep Bhatt; Suruchi Singh. "Cubic B-spline collocation method on a non-uniform mesh for solving nonlinear parabolic partial differential equation". سامانه مدیریت نشریات علمی, 10, 1, 1400, 28-43. doi: 10.22034/cmde.2020.39472.1726
Singh, Swarn, Bhatt, Sandeep, Singh, Suruchi. (1400). 'Cubic B-spline collocation method on a non-uniform mesh for solving nonlinear parabolic partial differential equation', سامانه مدیریت نشریات علمی, 10(1), pp. 28-43. doi: 10.22034/cmde.2020.39472.1726
Singh, Swarn, Bhatt, Sandeep, Singh, Suruchi. Cubic B-spline collocation method on a non-uniform mesh for solving nonlinear parabolic partial differential equation. سامانه مدیریت نشریات علمی, 1400; 10(1): 28-43. doi: 10.22034/cmde.2020.39472.1726

Cubic B-spline collocation method on a non-uniform mesh for solving nonlinear parabolic partial differential equation

Computational Methods for Differential Equations
مقاله 3، دوره 10، شماره 1، فروردین 2022، صفحه 28-43    اصل مقاله (261.21 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22034/cmde.2020.39472.1726
نویسندگان
Swarn Singh* 1؛ Sandeep Bhatt2؛ Suruchi Singh3
1Department of Mathematics, Sri Venkateswara College, University of Delhi, India.
2Department of Mathematics, University of Delhi, India.
3Department of Mathematics, Aditi Mahavidyalaya, University of Delhi, India.
چکیده
In this paper, an approximate solution of a nonlinear parabolic partial differential equation is obtained for a non-uniform mesh. The scheme for partial differential equation subject to Neumann boundary conditions is based on cubic B-spline collocation method. Modified cubic B-splines are proposed over non-uniform mesh to deal with the Dirichlet boundary conditions. This scheme produces a system of first order ordinary differential equations. This system is solved by Crank Nicholson method. The stability is also discussed using Von Neumann stability analysis. The accuracy and efficiency of the scheme are shown by numerical experiments. We have compared the approximate solutions with that in the literature.
کلیدواژه‌ها
Nonlinear parabolic partial differential equation؛ Collocation method؛ Cubic B-spline؛ Non-uniform mesh؛ Crank-Nicolson method
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