A numerical approach for solving the high-order nonlinear singular Emden-Fowler type equations

DOI10.1186/s13662-018-1529-7zbMath1446.65052OpenAlexW2807403309MaRDI QIDQ1712220

Taher Lotfi, Atta Dezhbord, Katayoun Mahdiani

Publication date: 21 January 2019

Published in: Advances in Difference Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/s13662-018-1529-7

zbMATH Keywords

reproducing kernel Hilbert space methodEmden-Fowler type equationsnonlinear singular initial value problems

Mathematics Subject Classification ID

Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations (34A12) Theoretical approximation of solutions to ordinary differential equations (34A45) Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) (46E22) Numerical solution of boundary value problems involving ordinary differential equations (65L10) Singular nonlinear boundary value problems for ordinary differential equations (34B16)

Related Items

Bernoulli collocation method for the third-order Lane-Emden-Fowler boundary value problem ⋮ Solving third-order Lane-Emden-Fowler equations using a variable stepsize formulation of a pair of block methods

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The variational iteration method for solving nonlinear singular boundary value problems arising in various physical models
• Solutions of singular IVPs of Lane-Emden type by homotopy perturbation method
• Solving a nonlinear system of second order boundary value problems
• A new efficient method for cases of the singular integral equation of the first kind
• Solving singular nonlinear second-order periodic boundary value problems in the reproducing kernel space
• A new method of solving the coefficient inverse problem
• Solutions of singular IVPs of Lane-Emden type by the variational iteration method
• A new reproducing kernel Hilbert space method for solving nonlinear fourth-order boundary value problems
• Rational Legendre pseudospectral approach for solving nonlinear differential equations of Lane-Emden type
• The exact solution for solving a class nonlinear operator equations in the reproducing kernel space.
• Numerical solutions of fractional differential equations of Lane-Emden type by an accurate technique
• Adomian decomposition method for a reliable treatment of the Emden-Fowler equation
• A new method for solving singular initial value problems in the second-order ordinary differential equations
• Stability and error analysis of the reproducing kernel Hilbert space method for the solution of weakly singular Volterra integral equation on graded mesh
• Representation of the exact solution for a kind of nonlinear partial differential equation
• Solving singular two-point boundary value problem in reproducing kernel space
• A computational method for solving third-order singularly perturbed boundary-value problems
• Representation of the exact solution for infinite system of linear equations
• SOLVING SINGULAR NONLINEAR TWO-POINT BOUNDARY VALUE PROBLEMS IN THE REPRODUCING KERNEL SPACE
• FURTHER STUDIES OF EMDEN'S AND SIMILAR DIFFERENTIAL EQUATIONS
• Solutions of nonlinear systems by reproducing kernel method
• Theory of Reproducing Kernels