Scopus İndeksli Yayınlar Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/8651

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Subject: search.filters.subject.Collocation MethodWoS Q: search.filters.wosQuartile.Q3

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  • Article
    Citation - Scopus: 17
    A Jacobi Collocation Method for Troesch's Problem in Plasma Physics
    (Editura Academiei Romane, 2014) Doha, E.H.; Baleanu, Dumitru; Baleanu, D.; Bhrawi, A.H.; Hafez, R.M.; Matematik
    In this paper, we propose a numerical approach for solving Troesch's problem which arises in the confinement of a plasma column by radiation pressure. It is also an inherently unstable two-point boundary value problem. The spatial approximation is based on shifted Jacobi-Gauss collocation method in which the shifted Jacobi-Gauss points are used as collocation nodes. The results presented here demonstrate reliability and efficiency of the method.
  • Article
    Citation - WoS: 27
    Citation - Scopus: 28
    An Efficient Collocation Technique for Solving Generalized Fokker-Planck Type Equations With Variable Coefficients
    (Editura Acad Romane, 2014) Bhrawy, A. H.; Baleanu, Dumitru; Ahmed, Engy A.; Baleanu, D.; Matematik
    This paper proposes an efficient numerical integration process for the generalized Fokker-Planck equation with variable coefficients. For spatial discretization the Jacobi-Gauss-Lobatto collocation (J-GL-C) method is implemented in which the Jacobi-Gauss-Lobatto points are used as collocation nodes for spatial derivatives. This approach has the advantage of obtaining the solution in terms of the Jacobi parameters alpha and beta. Using the above technique, the problem is reduced to the solution of a system of ordinary differential equations in tithe. This system can be also solved by standard numerical techniques. Our results demonstrate that the proposed method is a powerful algorithm for solving nonlinear partial differential equations.
  • Article
    Citation - WoS: 19
    Citation - Scopus: 18
    Efficient Jacobi-Gauss Collocation Method for Solving Initial Value Problems of Bratu Type
    (Pleiades Publishing inc, 2013) Bhrawy, A. H.; Baleanu, D.; Hafez, R. M.; Doha, E. H.
    In this paper, we propose the shifted Jacobi-Gauss collocation spectral method for solving initial value problems of Bratu type, which is widely applicable in fuel ignition of the combustion theory and heat transfer. The spatial approximation is based on shifted Jacobi polynomials J(n)((alpha, beta))(x) with alpha, beta is an element of (-1, infinity), x is an element of [0, 1] and n the polynomial degree. The shifted Jacobi-Gauss points are used as collocation nodes. Illustrative examples have been discussed to demonstrate the validity and applicability of the proposed technique. Comparing the numerical results of the proposed method with some well-known results show that the method is efficient and gives excellent numerical results.