On the convergence of finite-difference approximations to one-dimensional singular boundary-value problems

1970 ◽  
Vol 14 (4) ◽  
pp. 355-378 ◽  
Author(s):  
Pierre Jamet
Keyword(s):  
Finite Difference ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Singular Boundary ◽  
Singular Boundary Value Problems ◽  
One Dimensional ◽  
Finite Difference Approximations ◽  
Difference Approximations

HIGH ORDER ACCURATE QUINTIC NONPOLYNOMIAL SPLINE FINITE DIFFERENCE APPROXIMATIONS FOR THE NUMERICAL SOLUTION OF NON-LINEAR TWO POINT BOUNDARY VALUE PROBLEMS

2013 ◽  
Vol 05 (01) ◽  
pp. 1350018 ◽  
Author(s):  
NAVNIT JHA
Keyword(s):  
Finite Difference ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Computing Time ◽  
Diffusion Problem ◽  
High Order ◽  
Point Boundary ◽  
Finite Difference Approximations ◽  
Difference Approximations ◽  
Spline Basis

We develop a new sixth-order accurate numerical scheme for the solution of two point boundary value problems. The scheme uses nonpolynomial spline basis and high order finite difference approximations. With the help of spline functions, we derive consistency conditions and it is used to derive high order discretizations of the first derivative. The resulting difference schemes are solved by the standard Newton's method and have very small computing time. The new method is analyzed for its convergence and the efficiency of the proposed scheme is illustrated by convection-diffusion problem and nonlinear Lotka–Volterra equation. The order of convergence and maximum absolute errors are computed to present the utility of the new scheme.

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