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29 results on '"Hamid, Nur Nadiah Abd"'

1. Improved Order of Convergent of Cubic B-Spline collocation method for the nonlinear Schrödinger equation on single soliton.

Author

Ahmad, Azhar, Anuar, Hanis Safirah Saiful, Azmi, Amirah, Hamid, Nur Nadiah Abd, and Abbas, Muhammad

Subjects
NONLINEAR Schrodinger equation, INTERPOLATION spaces, COLLOCATION methods, FINITE difference method, ANALYTICAL solutions
Abstract

This paper applies the Improved Order of Convergent of the Cubic B-Spline collocation method (IOCuBSM) to obtain the numerical solution of the nonlinear Schrödinger Equation with a single soliton as the test problem. The approximate solution is based on the Crank-Nicolson scheme with the finite-difference method applied to time discretization and the improved order of convergent cubic B-Splines as the interpolation function in the space dimension. The error between numerical and analytical solutions is determined by discrete maximum norm and Euclidean norm and the method is proved to be unconditionally stable. Furthermore, the computational time for the methods is also studied. [ABSTRACT FROM AUTHOR]

Published
2024
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3. A numerical technique for solving time-fractional Navier-Stokes equation with Caputo's derivative using cubic B-spline functions.

Author

Okeke, Anthony Anya, Hamid, Nur Nadiah Abd, and Abbas, Muhammad

Subjects
*NAVIER-Stokes equations, *COLLOCATION methods, *NUMERICAL analysis, *FOURIER analysis, *PROBLEM solving
Abstract

In this study, a numerical technique for solving the generalized time-fractional Navier-Stokes equation in cylindrical coordinates via cubic B-spline (CBS) basis functions is proposed. The suggested technique for solving the problem is derived from the finite difference method and the collocation method. Caputo's derivative of order 0 < α ≤ 1 and CBS functions are employed for the time and spatial discretization, respectively. The Fourier stability analysis, derived from the von Neumann method was performed and indicate unconditionally stable. The convergence analysis of the presented numerical technique is of order O(h2 + Δt2−α). [ABSTRACT FROM AUTHOR]

Published
2024
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4. Besse Extended Cubic B-spline Collocation Method for Solving Benjamin-Bona-Mahony Equation.

Author

Rahan, Nur Nadiah Mohd and Hamid, Nur Nadiah Abd

Subjects
*COLLOCATION methods, *EQUATIONS, *LINEAR equations
Abstract

Extended cubic B-spline collocation method is formulated to solve the Benjamin-Bona-Mahony equation without linearization. The Besse relaxation scheme is applied on the nonlinear terms and therefore transforms the equation into a systemof two linear equations. The time derivative is discretized using Forward Difference Approximation whereas the spatial dimension is approximated using extended cubic B-spline function. Applying the von-Neumann stability analysis, the proposed technique are shown unconditionally stable. Two numerical examples are presented and the results are compared with the exact solutions and recent methods. [ABSTRACT FROM AUTHOR]

Published
2023
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25. Solving Boussinesq Equation Using Quintic B-spline and Quintic Trigonometric B-spline Interpolation Methods.

Author

Zakaria, Nur Fateha, Hassan, Nuraini Abu, Hamid, Nur Nadiah Abd, Majid, Ahmad Abd., and Ismail, Ahmad Izani Md.

Subjects
BOUSSINESQ equations, SPLINES, QUINTIC equations, TRIGONOMETRIC functions, INTERPOLATION, TRIGONOMETRIC interpolation
Abstract

The quintic B-spline (QBS) and quintic trigonometric B-spline (QTBS) functions are used to set up the collocation methods in finding solutions for the Boussinesq equation. The QBS and QTBS are applied as interpolating functions in the spatial dimension while the finite difference method (FDM) is used to discretize the time derivative. The nonlinear Boussinesq equation is linearized using Taylor's expansion. The von Neumann stability analysis is used to analyze the schemes and they are shown to be conditionally stable. In order to demonstrate the capability of the schemes, some problems are solved and compared with the analytical solutions and generated results from the FDM. The proposed numerical schemes are found to be accurate. [ABSTRACT FROM AUTHOR]

Published
2017
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26. Extended Cubic B-spline Interpolation Method Applied to Linear Two-Point Boundary Value Problems

Author

Hamid, Nur Nadiah Abd, Majid, Ahmad Abd., and Ahmad Izani Md. Ismail

Subjects
B-spline, two-point boundary value problem, extendedcubic B-spline
Abstract

Linear two-point boundary value problem of order two is solved using extended cubic B-spline interpolation method. There is one free parameters, λ, that control the tension of the solution curve. For some λ, this method produced better results than cubic B-spline interpolation method., {"references":["R. L. Burden and J. D. Faires, Numerical Analysis, 8th ed. Brooks/Cole,\nCengage Learning, 2005, pp. 641-647, 649-654, 656-660, 662-667, 668-\n682, 684-685.","Q. Fang, T. Tsuchiya, and T. Yamamoto, \"Finite difference,\nfinite element and finite volume methods applied to two-point\nboundary value problems,\" Journal of Computational and Applied\nMathematics, vol. 139, no. 1, pp. 9 - 19, 2002. (Online).\nAvailable: http://www.sciencedirect.com/science/article/B6TYH-\n44FD3DG-2/2/c59d6272888f882a64514091fff104dc","W. G. Bickley, \"Piecewise cubic interpolation and\ntwo-point boundary problems,\" The Computer Journal,\nvol. 11, no. 2, pp. 206-208, 1968. (Online). Available:\nhttp://comjnl.oxfordjournals.org/cgi/content/abstract/11/2/206","E. L. Albasiny and W. D. Hoskins, \"Cubic spline solutions\nto two-point boundary value problems,\" The Computer Journal,\nvol. 12, no. 2, pp. 151-153, 1969. (Online). Available:\nhttp://comjnl.oxfordjournals.org/cgi/content/abstract/12/2/151","D. J. Fyfe, \"The use of cubic splines in the solution of\ntwo-point boundary value problems,\" The Computer Journal,\nvol. 12, no. 2, pp. 188-192, 1969. (Online). Available:\nhttp://comjnl.oxfordjournals.org/cgi/content/abstract/12/2/188","H. Caglar, N. Caglar, and K. Elfaituri, \"B-spline interpolation\ncompared with finite difference, finite element and finite volume\nmethods which applied to two-point boundary value problems,\" Applied\nMathematics and Computation, vol. 175, no. 1, pp. 72 - 79, 2006.\n(Online). Available: http://www.sciencedirect.com/science/article/B6TY8-\n4H74KY7-1/2/60f26c55f79c0a39775e1d76586975da","G. Xu and G.-Z. Wang, \"Extended cubic uniform\nb-spline and (alpha)-b-spline,\" Acta Automatica Sinica,\nvol. 34, no. 8, pp. 980-984, Aug. 2008. (Online).\nAvailable: http://www.sciencedirect.com/science/article/B8H0V-\n4T6VT15-3/2/7c4718af9afe2c6bae6b0d1d4f8e66e3"]}

Published
2010
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29. Splines For Linear Two-Point Boundary Value Problems

Author

Hamid, Nur Nadiah Abd and Hamid, Nur Nadiah Abd

Abstract

Linear two-point boundary value problems of order two are solved using cubic trigonometric B-spline, cubic Beta-spline and extended cubic B-spline interpolation methods. Cubic Beta-spline has two shape parameters, b1 and b2 while extended cubic B-spline has one, l . In this method, the parameters were varied and the corresponding approximations were compared to the exact solution to obtain the best values of b1, b2 and l . The methods were tested on four problems and the obtained approximated solutions were compared to that of cubic B-spline interpolation method. Trigonometric B-spline produced better approximation for problems with trigonometric form whereas Beta-spline and extended cubic B-spline produced more accurate approximation for some values of b1, b2 and l . All in all, extended cubic B-spline interpolation produced the most accurate solution out of the three splines. However, the method of finding l cannot be applied in the real world because there is no exact solution provided. That method was implemented in order to test whether values of l that produce better approximation do exist. Thus, an approach of finding optimized l is developed and Newton’s method was applied to it. This approach was found to approximate the solution much better than cubic B-spline interpolation method.

Published
2010

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