scholarly journals Solving the Lane–Emden Equation within a Reproducing Kernel Method and Group Preserving Scheme

Mathematics ◽  
2017 ◽  
Vol 5 (4) ◽  
pp. 77 ◽  
Author(s):  
Mir Hashemi ◽  
Ali Akgül ◽  
Mustafa Inc ◽  
Idrees Mustafa ◽  
Dumitru Baleanu
Keyword(s):  
Reproducing Kernel ◽  
Kernel Method ◽  
Reproducing Kernel Method ◽  
Emden Equation ◽  
Group Preserving Scheme

scholarly journals A Unified Reproducing Kernel Method and Error Estimation for Solving Linear Differential Equation with Functional Constraints

2015 ◽  
Vol 2015 ◽  
pp. 1-9
Author(s):  
Xinjian Zhang ◽  
Xiongwei Liu
Keyword(s):  
Differential Equation ◽  
Approximate Solution ◽  
Linear Differential Equation ◽  
Error Estimation ◽  
Reproducing Kernel ◽  
Kernel Method ◽  
Inner Product ◽  
Reproducing Kernel Method ◽  
Linear Differential ◽  
Polynomial Reproducing

A unified reproducing kernel method for solving linear differential equations with functional constraint is provided. We use a specified inner product to obtain a class of piecewise polynomial reproducing kernels which have a simple unified description. Arbitrary order linear differential operator is proved to be bounded about the special inner product. Based on space decomposition, we present the expressions of exact solution and approximate solution of linear differential equation by the polynomial reproducing kernel. Error estimation of approximate solution is investigated. Since the approximate solution can be described by polynomials, it is very suitable for numerical calculation.

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