iosr-Jm   Volume-4 ~ Issue-6

Abstract: Recently the unified method for finding traveling wave solutions of non-linear evolution equations was proposed by one of the authors a. It was shown that, this method unifies all the methods being used to find these solutions. In this paper, we extend this method to find a class of formal exact solutions to Korteweg-de Vries (KdV) equation with space dependent coefficients. A new class of multiple-soliton or wave trains is obtained.
Keywords: Exact solution, Extended unified method, Korteweg-deVries equation, variable coefficients

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Abstract:A self- starting hybrid linear multistep method for direct solution of the general second-order initial value problem is considered. The continuous method is used to obtain Multiple Finite Difference Methods (MFDMs) (each of order 7) which are combined as simultaneous numerical integrators to provide a direct solution to IVPs over sub-intervals which do not overlap. The convergence of the MFDMs is discussed by conveniently representing the MFDMs as a block method and verifying that the block method is zero-stable and consistent. The superiority of the MFDMs over published work is established numerically.
Keywords: Multiple Finite Difference Methods, Second Order, Boundary Value Problem, Block Methods, Multistep Methods

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Comput Math., 8: 985-991. DOI: 10.1080/0020716031000079572
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formula of order four for an initial value problem,. J.Computat. Applied Math., 175: 369-373. DOI: 10.1016/j.cam.2004.06.016.
[6] Jator, S.N(2007). A sixth order linear multistep method for the direct solution of y00 = f(x, y, y0), International Journal of Pure and
Applied Mathematics, 40, No. 4, 457-472.
[7] Jator, S.N and Li, J (2007) A self-starting linear multistep method for a direct solution of the general second order initial value
problem, International Journal of Computer Mathematics Vol. 86, No. 5, May 2009, 827–836
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Pure and Applied Mathematics, 43, No. 2, 253 - 265.
[9] Mohammmed, U.,Jiya, M and Mohammed, A.A(2010). A class of six step block method for solution of general second order
ordinary differential equations, Pacific Journal of Science and Technology. 11(2):pp273-277.
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of Nigerian Mathematical Society (JNMS). vol 30 p 25-39

Abstract:This paper deals with the determination of thermal stresses in a thin clamped hollow disk under unsteady temperature field due to point heat source situated at centre along radial and axial direction within it. A thin hollow disk is considered having arbitrary initial temperature and is subjected to arbitrary heat flux at the outer circular boundary; whereas inner boundary is at zero heat flux. Also, the upper and lower surfaces of the disk are at zero temperature. The inner and outer edges of the disk are clamped. The governing heat conduction equation has been solved by the method of integral transform technique. The results are obtained in a series form in terms of Bessel's functions. The results have been computed numerically and illustrated graphically.

Keywords: Heat Conduction, Point Heat Source, Thermal Stresses, clamped hollow disk, Unsteady Temperature

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Abstract: As generalization of the fractional Cosine transform (FRCT), the Canonical Cosine Transform (CCT) has been used in several areas, including optical analysis and signal processing. For practical purpose half canonical cosine transform is more useful. Hence in this paper we have proved some important results Differentiation property, Modulation property, Scaling property, Derivative property, Parseval's Identity for half canonical cosine transform (HCCT).
Keywords: Linear canonical transform, Fractional Fourier Transform.

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