Accurate solution of the Thomas-Fermi equation using the fractional order of rational Chebyshev functions
DOI10.1016/j.cam.2016.11.035zbMath1362.34039OpenAlexW2561161192MaRDI QIDQ508037
Kourosh Parand, Mehdi Delkhosh
Publication date: 9 February 2017
Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.cam.2016.11.035
collocation methodquasilinearization methodnonlinear ODEsemi-infinite domainThomas-Fermi equationfractional order of rational Chebyshev functions
Theoretical approximation of solutions to ordinary differential equations (34A45) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Numerical solution of boundary value problems involving ordinary differential equations (65L10) Singular nonlinear boundary value problems for ordinary differential equations (34B16) Boundary value problems on infinite intervals for ordinary differential equations (34B40)
Related Items (23)
Cites Work
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- Solving Volterra's population growth model of arbitrary order using the generalized fractional order of the Chebyshev functions
- Finite difference/finite element method for two-dimensional space and time fractional Bloch-Torrey equations
- Solving a laminar boundary layer equation with the rational Gegenbauer functions
- An asymptotic analysis of positive solutions of generalized Thomas-Fermi differential equations - the sub-half-linear case
- The existence of solutions to second-order singular boundary value problems
- The improved homotopy analysis method for the Thomas-Fermi equation
- Analytic solutions of some self-adjoint equations by using variable change method and its applications
- Solution of the Thomas-Fermi equation with a convergent approach
- The sinc-collocation method for solving the Thomas-Fermi equation
- A finite element method for singular solutions of the Navier-Stokes equations on a non-convex polygon
- Multiquadrics - a scattered data approximation scheme with applications to computational fluid-dynamics. I: Surface approximations and partial derivative estimates
- Series solution to the Thomas-Fermi equation
- A new analytical and numerical treatment for singular two-point boundary value problems via the Adomian decomposition method
- Rational approximation to the Thomas-Fermi equations
- Rational Chebyshev pseudospectral approach for solving Thomas-Fermi equation
- Analytic continuation of Taylor series and the boundary value problems of some nonlinear ordinary differential equations
- A Chebyshev spectral method based on operational matrix for initial and boundary value problems of fractional order
- An adaptive algorithm for the Thomas-Fermi equation
- Positive solutions of fourth order Thomas-Fermi type differential equations in the framework of regular variation
- Piecewise quasilinearization techniques for singular boundary-value problems
- Applications of density matrix in the fractional quantum mechanics: Thomas-Fermi model and Hohenberg-Kohn theorems revisited
- Solution of a laminar boundary layer flow via a numerical method
- Collocation method using sinc and rational Legendre functions for solving Volterra's population model
- Variation and series approach to the Thomas-Fermi equation
- Numerical solution of the Klein-Gordon equation via He's variational iteration method
- Pricing European and American options using a very fast and accurate scheme: the meshless local Petrov-Galerkin method
- Pricing European and American options by radial basis point interpolation
- Local weak form meshless techniques based on the radial point interpolation (RPI) method and local boundary integral equation (LBIE) method to evaluate European and American options
- Computational aspects of pseudospectral Laguerre approximations
- Exp-function method for nonlinear wave equations
- Large-degree asymptotics and exponential asymptotics for Fourier, Chebyshev and Hermite coefficients and Fourier transforms
- Application of the Adomian decomposition method for the Fokker-Planck equation
- Solution of the Thomas-Fermi equation
- The optimization of convergence for Chebyshev polynomial methods in an unbounded domain
- Oscillatory and asymptotic properties of solutions of generalized Thomas- Fermi equations with deviating arguments
- Chebyshev series solution of the Thomas-Fermi equation
- Variational approach to the Thomas-Fermi equation
- An explicit analytic solution to the Thomas-Fermi equation.
- Laguerre-Galerkin method for nonlinear partial differential equations on a semi-infinite interval
- Symmetry results for finite-temperature, relativistic Thomas-Fermi equations
- A coupling method of a homotopy technique and a perturbation technique for nonlinear problems
- Accurate calculation of the solutions to the Thomas-Fermi equations
- Nonlinearities distribution homotopy perturbation method applied to solve nonlinear problems: Thomas-Fermi equation as a case study
- Relativistic formulation of the generalized nonextensive Thomas-Fermi model
- Numerical study of astrophysics equations by meshless collocation method based on compactly supported radial basis function
- The modified decomposition method and Padé approximants for solving the Thomas-Fermi equation
- Multiquadrics -- a scattered data approximation scheme with applications to computational fluid-dynamics. II: Solutions to parabolic, hyperbolic and elliptic partial differential equations
- Orthogonal rational functions on a semi-infinite interval
- Spectral methods using rational basis functions on an infinite interval
- Homotopy perturbation method: a new nonlinear analytical technique
- Rational Chebyshev series for the Thomas-Fermi function: endpoint singularities and spectral methods
- Jacobi approximations in certain Hilbert spaces and their applications to singular differential equations
- Homotopy perturbation technique
- Existence of positive solutions for a generalized and fractional ordered Thomas-Fermi theory of neutral atoms
- On the rational second kind Chebyshev pseudospectral method for the solution of the Thomas-Fermi equation over an infinite interval
- Laguerre pseudospectral approximation to the Thomas-Fermi equation
- Decreasing regularly varying solutions of sublinearly perturbed superlinear Thomas-Fermi equation
- Operation matrix method based on Bernstein polynomials for the Riccati differential equation and Volterra population model
- Optimal control of a parabolic distributed parameter system via radial basis functions
- Rational and exponential Legendre Tau method on steady flow of a third grade fluid in a porous half space
- Spectral method for solving the nonlinear Thomas-Fermi equation based on exponential functions
- Quasilinearization method and summation of the WKB series
- Increasing solutions of Thomas-Fermi type differential equations--the superlinear case
- A series solution to the Thomas-Fermi equation
- Some aspects of the Thomas-Fermi equation
- Analytical solution of the transpiration on the boundary layer flow and heat transfer over a vertical slender cylinder
- An improved numerical method for a class of astrophysics problems based on radial basis functions
- Numerical approximations for population growth model by rational Chebyshev and Hermite functions collocation approach: A comparison
- Numerical solution of hyperbolic telegraph equation using the Chebyshev tau method
- Quasilinearization approach to the resonance calculations: the quartic oscillator
- An exact result for the Thomas–Fermi equation:a prioribounds for the potential slope at the origin
- Scattered Data Interpolation: Tests of Some Method
- Approximation of Some Diffusion Evolution Equations in Unbounded Domains by Hermite Functions
- New explicit finite difference schemes for two-dimensional diffusion subject to specification of mass
- Thomas-Fermi Equation Solution by the Differential Analyzer
- Quasilinearization method and its verification on exactly solvable models in quantum mechanics
- An analytic solution to the Thomas–Fermi equation
- The Thomas-Fermi Method for Metals
- Monotonous enclosures for the Thomas-Fermi equation in the isolated neutral atom case
- The numerical study on the unsteady flow of gas in a semi-infinite porous medium using an RBF collocation method
- A Complete Orthonormal System of Functions in $L^2 ( - \infty ,\infty )$ Space
- The Evaluation and Estimation of the Coefficients in the Chebyshev Series Expansion of a Function
- Momenta in Atoms using the Thomas-Fermi Method
- Equations of State of Elements Based on the Generalized Fermi-Thomas Theory
- A rational approximation and its applications to differential equations on the half line
- Quasilinearization approach to nonlinear problems in physics with application to nonlinear ODEs
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