A spline interpolation method for solving boundary value problems of potential theory from discretely given data

1987 ◽  
Vol 3 (1) ◽  
pp. 27-50
Author(s):  
Willi Freeden
Keyword(s):  
Boundary Value Problems ◽  
Potential Theory ◽  
Interpolation Method ◽  
Spline Interpolation ◽  
Boundary Value

scholarly journals New Cubic B-Spline Approximation for Solving Linear Two-Point Boundary-Value Problems

Mathematics ◽  
2021 ◽  
Vol 9 (11) ◽  
pp. 1250
Author(s):  
Busyra Latif ◽  
Samsul Ariffin Abdul Abdul Karim ◽  
Ishak Hashim
Keyword(s):  
Boundary Value Problems ◽  
Least Squares Method ◽  
Interpolation Method ◽  
Spline Interpolation ◽  
Boundary Value ◽  
Spline Approximation ◽  
Second Order ◽  
Order Derivative ◽  
Point Boundary ◽  
B Spline

In this study, we introduce a new cubic B-spline (CBS) approximation method to solve linear two-point boundary value problems (BVPs). This method is based on cubic B-spline basis functions with a new approximation for the second-order derivative. The theoretical new approximation for a second-order derivative and the error analysis have been successfully derived. We found that the second-order new approximation was O(h3) accurate. By using this new second-order approximation, the proposed method was O(h5) accurate. Four numerical problems consisting of linear ordinary differential equations and trigonometric equations with different step sizes were performed to validate the accuracy of the proposed methods. The numerical results were compared with the least squares method, finite difference method, finite element method, finite volume method, B-spline interpolation method, extended cubic B-spline interpolation method and the exact solutions. By finding the maximum errors, the results consistently showed that the proposed method gave the best approximations among the existing methods. We also found that our proposed method involved simple implementation and straightforward computations. Hence, based on the results and the efficiency of our method, we can say that our method is reliable and a promising method for solving linear two-point BVPs.

Mixed Boundary Value Problems in Potential Theory

1968 ◽  
Vol 52 (382) ◽  
pp. 417
Author(s):  
G. E. Hunt ◽  
I. N. Sneddon
Keyword(s):  
Boundary Value Problems ◽  
Potential Theory ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Mixed Boundary Value Problems
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