scholarly journals Spline collocation approach to study Brachistochrone problem

2019 ◽  
Vol 38 (2) ◽  
pp. 353-362
Author(s):  
Pinky M. Shah ◽  
Jyotindra C. Prajapati
Keyword(s):  
Spline Collocation ◽  
Brachistochrone Problem ◽  
Collocation Approach

scholarly journals Application of Hybrid Cubic B-Spline Collocation Approach for Solving a Generalized Nonlinear Klien-Gordon Equation

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Shazalina Mat Zin ◽  
Ahmad Abd Majid ◽  
Ahmad Izani Md. Ismail ◽  
Muhammad Abbas
Keyword(s):  
Approximate Solution ◽  
Space Dimension ◽  
Gordon Equation ◽  
Time Derivative ◽  
Test Problems ◽  
Spline Collocation ◽  
B Spline ◽  
Implicit Approach ◽  
Collocation Approach ◽  
Good Agreement

The generalized nonlinear Klien-Gordon equation is important in quantum mechanics and related fields. In this paper, a semi-implicit approach based on hybrid cubic B-spline is presented for the approximate solution of the nonlinear Klien-Gordon equation. The usual finite difference approach is used to discretize the time derivative while hybrid cubic B-spline is applied as an interpolating function in the space dimension. The results of applications to several test problems indicate good agreement with known solutions.

A cubic trigonometric B-spline collocation approach for the fractional sub-diffusion equations

2017 ◽  
Vol 293 ◽  
pp. 311-319 ◽  
Author(s):  
Muhammad Yaseen ◽  
Muhammad Abbas ◽  
Ahmad Izani Ismail ◽  
Tahir Nazir
Keyword(s):  
Diffusion Equations ◽  
Spline Collocation ◽  
B Spline ◽  
Collocation Approach

SPLINE TECHNIQUES FOR SOLVING RELATIVISTIC CONSERVATION EQUATIONS

1993 ◽  
Vol 04 (04) ◽  
pp. 723-747 ◽  
Author(s):  
D. J. DEAN ◽  
C. BOTTCHER ◽  
M. R. STRAYER
Keyword(s):  
Three Dimensional ◽  
Heavy Ion ◽  
Analytic Solutions ◽  
Numerical Results ◽  
Relativistic Heavy Ion Collisions ◽  
Spline Collocation ◽  
One Dimensional ◽  
Ion Collisions ◽  
Collocation Approach ◽  
The One

We discuss a new numerical method for solving the relativistic hydrodynamic equations based upon the basis-spline collocation approach. Analytical and numerical results are compared for several problems, including one-dimensional expansions and collisions for which analytical solutions exist. Our methods, which may be easily and massively parallelized, are shown to give numerical results which agree to within a few percent of the analytic solutions. We discuss the relevance of the υ = z/t scaling solutions for the one-dimensional problem when applied to relativistic heavy-ion collisions. Finally, we discuss applications to three-dimensional problems, and present results for a typical three-dimensional expansion.

scholarly journals NUMERICAL SOLUTION OF A CLASS OF NONLINEAR SYSTEM OF SECOND-ORDER BOUNDARY-VALUE PROBLEMS: A FOURTH-ORDER CUBIC SPLINE APPROACH

2015 ◽  
Vol 20 (5) ◽  
pp. 681-700 ◽  
Author(s):  
Suheil A. Khuri ◽  
Ali M. Sayfy
Keyword(s):  
Numerical Solution ◽  
Boundary Value Problems ◽  
Fourth Order ◽  
Numerical Solutions ◽  
Boundary Value ◽  
Second Order ◽  
Spline Collocation ◽  
Extended System ◽  
Collocation Approach ◽  
Linear And Nonlinear

A cubic B-spline collocation approach is described and presented for the numerical solution of an extended system of linear and nonlinear second-order boundary-value problems. The system, whether regular or singularly perturbed, is tackled using a spline collocation approach constructed over uniform or non-uniform meshes. The rate of convergence is discussed theoretically and verified numerically to be of fourth-order. The efficiency and applicability of the technique are demonstrated by applying the scheme to a number of linear and nonlinear examples. The numerical solutions are contrasted with both analytical and other existing numerical solutions that exist in the literature. The numerical results demonstrate that this method is superior as it yields more accurate solutions.

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