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Search Results: 1 - 10 of 242194 matches for " Pedro Pablo Cárdenas Alzate "
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An Iterative Method for Solving Two Special Cases of Lane-Emden Type Equation  [PDF]
Pedro Pablo Cárdenas Alzate
American Journal of Computational Mathematics (AJCM) , 2014, DOI: 10.4236/ajcm.2014.43021
Abstract:

In this work we apply the differential transformation method or DTM for solving some classes of Lane-Emden type equations as a model for the dimensionless density distribution in an isothermal gas sphere \"\" and as a study of the gravitational potential of (white-dwarf) stars ,\"\" which are nonlinear ordinary differential equations on the semi-infinite domain [1] [2]. The efficiency of the DTM is illustrated by investigating the convergence results for this type of the Lane-Emden equations. The numerical results show the reliability and accuracy of this method.

A Survey of the Implementation of Numerical Schemes for Linear Advection Equation  [PDF]
Pedro Pablo Cárdenas Alzate
Advances in Pure Mathematics (APM) , 2014, DOI: 10.4236/apm.2014.48052
Abstract:

The interpolation method in a semi-Lagrangian scheme is decisive to its performance. Given the number of grid points one is considering to use for the interpolation, it does not necessarily follow that maximum formal accuracy should give the best results. For the advection equation, the driving force of this method is the method of the characteristics, which accounts for the flow of information in the model equation. This leads naturally to an interpolation problem since the foot point is not in general located on a grid point. We use another interpolation scheme that will allow achieving the high order for the box initial condition.

A Survey of the Implementation of Numerical Schemes for the Heat Equation Using Forward Euler in Time  [PDF]
Pedro Pablo Cárdenas Alzate
Journal of Applied Mathematics and Physics (JAMP) , 2014, DOI: 10.4236/jamp.2014.213135
Abstract: We establish the conditions for the compute of the Global Truncation Error (GTE), stability restriction on the time step and we prove the consistency using forward Euler in time and a fourth order discretization in space for Heat Equation with smooth initial conditions and Dirichlet boundary conditions.
A Special Case of Variational Formulation for Two-Point Boundary Value Problem in L2(Ω)  [PDF]
Pedro Pablo Cárdenas Alzate
Applied Mathematics (AM) , 2015, DOI: 10.4236/am.2015.64065
Abstract: We consider the nonlinear boundary value problems for elliptic partial differential equations and using a maximum principle for this problem we show uniqueness and continuous dependence on data. We use the strong version of the maximum principle to prove that all solutions of two-point BVP are positives and we also show a numerical example by applying finite difference method for a two-point BVP in one dimension based on discrete version of the maximum principle.
The Zhou’s Method for Solving the White-Dwarfs Equation  [PDF]
Pedro Pablo Cárdenas Alzate, William Ardila Urue?a
Applied Mathematics (AM) , 2013, DOI: 10.4236/am.2013.410A3005
Abstract:

In this work we apply the differential transformation method (Zhous method) or DTM for solving white-dwarfs equation which Chandrasekhar [1] introduced in his study of the gravitational potential of these degenerate (white-dwarf) stars. DTM may be considered as alternative and efficient for finding the approximate solutions of the initial values problems. We prove superiority of this method by applying them on the some Lane-Emden type equation, in this case\"\". The power series solution of the reduced equation transforms into an approximate implicit solution of the original equation.

A Two-Point Boundary Value Problem by Using a Mixed Finite Element Method  [PDF]
Pedro Pablo Cárdenas Alzate, José Rodrigo González Granada
Applied Mathematics (AM) , 2015, DOI: 10.4236/am.2015.612177
Abstract: This paper describes a numerical solution for a two-point boundary value problem. It includes an algorithm for discretization by mixed finite element method. The discrete scheme allows the utilization a finite element method based on piecewise linear approximating functions and we also use the barycentric quadrature rule to compute the stiffness matrix and the L2-norm.
An iterative method for a second order problem with nonlinear two-point boundary conditions
Pablo Amster,Pedro Pablo Cárdenas Alzate
Matemáticas : Ense?anza Universitaria , 2011,
Abstract: A semi-linear second order ODE under a nonlinear two-point boundary condition is considered. Under appropriate conditions on the nonlinear term of the equation, we define a two-dimensional shooting argument which allows to obtain solutions for some specific situations by the use of Poincaré-Miranda's theorem. Finally, we apply this result combined with the method of upper and lower solutions and develop an iterative sequence that converges to a solution of the problem.
A Special Case on the Stability and Accuracy for the 1D Heat Equation Using 3-Level and θ-Schemes  [PDF]
Pedro Pablo Cárdenas Alzate, José Gerardo Cardona, Luz María Rojas
Applied Mathematics (AM) , 2015, DOI: 10.4236/am.2015.63045
Abstract: We establish the conditions for the compute of the stability restriction and local accuracy on the time step and we prove the consistency and local truncation error by using θ-scheme and 3-level scheme for Heat Equation with smooth initial conditions and for some parameter θ∈[0,1].
The Zhou’s Method for Solving the Euler Equidimensional Equation  [PDF]
Pedro Pablo Cárdenas Alzate, Jhon Jairo León Salazar, Carlos Alberto Rodríguez Varela
Applied Mathematics (AM) , 2016, DOI: 10.4236/am.2016.717172
Abstract: In this work, we apply the Zhou’s method [1] or differential transformation method (DTM) for solving the Euler equidimensional equation. The Zhou’s method may be considered as alternative and efficient for finding the approximate solutions of initial values problems. We prove superiority of this method by applying them on the some Euler type equation, in this case of order 2 and 3 [2]. The power series solution of the reduced equation transforms into an approximate implicit solution of the original equations. The results agreed with the exact solution obtained via transformation to a constant coefficient equation.
ALGUNOS RESULTADOS DE OPERADORES LINEALES CONTINUOS
EDGAR ALIRIO VALENCIA,FERNANDO MESA,PEDRO PABLO CáRDENAS ALZATE
Scientia Et Technica , 2009,
Abstract: En este artículo se presentan dos resultados interesantes de operadores continuos en un espacio de Hilbert.
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