Geodesic
Spline in tension method for non-linear two point boundary value problems on a geometric mesh
Matematičeskoe modelirovanie, Tome 27 (2015) no. 3, pp. 33-48

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In this paper, we discuss a new method based on spline in tension approximation for the numerical solution of two-point non-linear boundary value problems on uniform mesh. The method is of order four. We have discussed the derivation and the convergence of the proposed method in detail. The method is extended to non-uniform mesh. Numerical results are given to illustrate the efficiency of the proposed method.
Keywords: Spline in tension; Non polynomial spline; Convergence analysis; Root mean square errors; Variable mesh; Burgers’ equation. 
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     author = {J. Talwar and R. K. Mohanty},
     title = {Spline in tension method for non-linear two point boundary value problems on a geometric mesh},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {33--48},
     publisher = {mathdoc},
     volume = {27},
     number = {3},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/MM_2015_27_3_a2/}
}
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J. Talwar; R. K. Mohanty. Spline in tension method for non-linear two point boundary value problems on a geometric mesh. Matematičeskoe modelirovanie, Tome 27 (2015) no. 3, pp. 33-48. http://geodesic.mathdoc.fr/item/MM_2015_27_3_a2/