Ghazala Akram
University of the Punjab
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Featured researches published by Ghazala Akram.
Applied Mathematics and Computation | 2006
Shahid S. Siddiqi; Ghazala Akram
Abstract Non-polynomial spline is used for the numerical solutions of the 12th order linear special case boundary value problems. The end conditions are derived for the definition of spline. Siddiqi and Twizell [S.S. Siddiqi, E.H. Twizell, Spline solutions of linear twelfth-order boundary value problems, Int. J. Comput. Math. 78 (1998) 345–362] presented the solutions of 12th order boundary value problems using 12th degree spline, where some unexpected results for the solution and its derivatives were obtained, near the boundaries of the interval. No such situation is observed in this method, near the boundaries of the interval and the results are better in the whole interval. Out of three, two examples compared with that considered by Siddiqi and Twizell (1998), show that the method developed in the paper is more efficient.
Numerical Algorithms | 2013
Ghazala Akram; Hamood Ur Rehman
In this paper, the approximate solutions to the eighth-order boundary-value problems are presented using the reproducing kernel space method. The procedure is applied on both linear and nonlinear problems. Searching least value (SLV) method is investigated for nonlinear boundary value problems. The argument is based on the reproducing kernel space
Applied Mathematics and Computation | 2006
Shahid S. Siddiqi; Ghazala Akram
W_{2}^{9}[a,b]
Applied Mathematics and Computation | 2006
Ghazala Akram; Shahid S. Siddiqi
. The approach provides the solution in the form of a convergent series with easily computable components. Analytical results are given for several examples to illustrate the implementation and efficiency of the method. A comparison of the results obtained by the present method with results obtained by other methods reveals that the present method is more effective and convenient.
Applied Mathematics and Computation | 2007
Shahid S. Siddiqi; Ghazala Akram
Abstract Nonpolynomial spline is used for the numerical solutions of the fifth order linear special case boundary value problems. End conditions for the definition of spline are taken from Siddiqi and Akram [S.S. Siddiqi, Ghazala Akram, Sextic spline solutions of fifth order boundary value problems, Appl. Math. Lett., submitted for publication], consistent with the fifth order boundary value problem. Caglar et al. [H.N. Caglar, S.H. Caglar, E.H. Twizell, The numerical solution of fifth-order boundary-value problems with sixth-degree B-spline functions, Appl. Math. Lett. 12 (1999) 25–30] presented the solution of fifth order boundary value problem using sixth degree B-spline, is first order convergent. The method presented in this paper is observed to be a second order convergent. For the numerical illustration of the method developed, an example has also been considered.
International Journal of Computer Mathematics | 2007
Shahid S. Siddiqi; Ghazala Akram
Nonic spline is used for the numerical solutions of the eighth order linear special case boundary value problems. The end conditions are derived for the definition of spline. The algorithm developed not only approximates the solutions, but their higher order derivatives as well. The method presented in this paper has also been proved to be second order convergent. Two examples compared with those considered by Inc et al. [M. Inc, D.J. Evans, An efficient approach to approximate solutions of eighth-order boundary-value problems, Int. J. Comput. Math. 81 (6) (2004) 685-692] and Siddiqi et al. [S.S. Siddiqi, E.H. Twizell, Spline solution of linear eighth-order boundary value problems, Comput. Methods Appl. Mech. Eng. 131 (1996) 309-325], show that the method developed in this paper is more efficient.
Applied Mathematics and Computation | 2007
Shahid S. Siddiqi; Ghazala Akram; Saima Nazeer
Abstract Numerical solutions of the tenth-order linear special case boundary value problems are obtained using eleventh degree spline. The end conditions consistent with the BVP, are also derived. Siddiqi and Twizell [S.S. Siddiqi, E.H. Twizell, Spline solutions of linear tenth order boundary value problems, Int. J. Comput. Math. 68 (1998) 345–362] presented the solutions of tenth-order boundary value problems using tenth degree spline, where some unexpected results for the solution and higher order derivatives were obtained near the boundaries of the interval. No such unexpected situation is observed in this method, near the boundaries of the interval and the results are better in the whole interval. The algorithm developed approximates the solutions, and their higher order derivatives. Numerical illustrations are tabulated to compare the errors with those considered by Siddiqi and Twizell [S.S. Siddiqi, E.H. Twizell, Spline solutions of linear tenth order boundary value problems, Int. J. Comput. Math. 68 (1998) 345–362] and the method is observed to be better.
Applied Mathematics and Computation | 2008
Shahid S. Siddiqi; Ghazala Akram; Arfa Elahi
The non-polynomial spline technique is used for the numerical solution of eighth-order linear special case boundary value problems. The method presented in this paper has also been proven to be second-order convergent. To compare the method developed in this paper with those developed by Inc and Evans, and Siddiqi and Twizell, two examples are considered and it is observed that our method is more efficient.
Applied Mathematics and Computation | 2006
Shahid S. Siddiqi; Ghazala Akram
Abstract There are few techniques available to numerically solve sixth-order boundary value problems with two point boundary conditions. In this paper, quintic spline method is developed for the numerical solutions of linear special case sixth-order boundary value problems. Two examples are considered for the numerical illustration of the method developed. The method is also compared with those developed by EL-Gamel et al. [Mohamed EL-Gamel, John R. Cannon, Ahmed I. Zayed, Sinc–Galerkin method for solving sixth-order BVPs, Math. Comput. 73 (247) (2003)] and Wazwaz [A. Wazwaz, The numerical solution of sixth-order boundary value problems by the modified decomposition method, Appl. Math. Comput. 118 (2001) 311–325]. The comparison shows that the quintic spline method is more efficient and effective tool and yields better results.
Applied Mathematics and Computation | 2007
Shahid S. Siddiqi; Ghazala Akram
Abstract Some techniques are available to solve numerically fifth order boundary value problems with two point boundary condition. This paper describes quartic spline method for the numerical solution of linear special case fifth order boundary value problem. Three examples are considered for the numerical illustration of the method developed. The method is also compared with that developed by Caglar et al. [H.N. Caglar, S.H. Caglar, E.H. Twizell, The numerical solution of fifth order boundary value problems with sixth degree B-Spline functions, Appl. Math. Lett. 12 (1999) 25–30] and Khan [M.S. Khan, Finite difference solutions of fifth order boundary value problems, Ph.D. thesis, Brunal University, England, 1994]. This comparison provides that developed method is more efficient that effective tool and yields better results.