Spline-in-compression approximation of order of accuracy three (four) for second order non-linear IVPs on a graded mesh
A spline-in-compression method, implicit in nature, for computing numerical solution of second order nonlinear initial-value problems (IVPs) on a mesh not necessarily equidistant is discussed. The proposed estimation has been derived directly from consistency condition which is third-order accurate....
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Elsevier
2023-12-01
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| Series: | MethodsX |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2215016123003059 |
| _version_ | 1797405428395540480 |
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| author | R.K. Mohanty Bishnu Pada Ghosh |
| author_facet | R.K. Mohanty Bishnu Pada Ghosh |
| author_sort | R.K. Mohanty |
| collection | DOAJ |
| description | A spline-in-compression method, implicit in nature, for computing numerical solution of second order nonlinear initial-value problems (IVPs) on a mesh not necessarily equidistant is discussed. The proposed estimation has been derived directly from consistency condition which is third-order accurate. For scientific computation, we use monotonically descending step lengths. The suggested method is applicable to a wider range of physical problems including the problems which are singular in nature. This is possible due to off-step discretization employed in the spline technique. We examine the absolute stability and super-stability of the method when applied to a problem of physical significances. We have shown that the method is absolutely stable in the case of graded mesh and super stable in the case of constant mesh. The advantage of our method lies in it being highly cost and time effective, as we employ a three-point compact stencil, thereby reducing the algebraic calculations considerably. The proposed method which is applicable to singular, boundary layer and singularly perturbed problems is a research gap which we overcame by proposing this new compact spline method. |
| first_indexed | 2024-03-09T03:09:47Z |
| format | Article |
| id | doaj.art-40d9163d496c4cb4a625d079f1fa9d52 |
| institution | Directory Open Access Journal |
| issn | 2215-0161 |
| language | English |
| last_indexed | 2024-03-09T03:09:47Z |
| publishDate | 2023-12-01 |
| publisher | Elsevier |
| record_format | Article |
| series | MethodsX |
| spelling | doaj.art-40d9163d496c4cb4a625d079f1fa9d522023-12-04T05:22:16ZengElsevierMethodsX2215-01612023-12-0111102308Spline-in-compression approximation of order of accuracy three (four) for second order non-linear IVPs on a graded meshR.K. Mohanty0Bishnu Pada Ghosh1Department of Mathematics, South Asian University, New Delhi 110068, IndiaDepartment of Mathematics, Jagannath University, Dhaka, Bangladesh; Corresponding author.A spline-in-compression method, implicit in nature, for computing numerical solution of second order nonlinear initial-value problems (IVPs) on a mesh not necessarily equidistant is discussed. The proposed estimation has been derived directly from consistency condition which is third-order accurate. For scientific computation, we use monotonically descending step lengths. The suggested method is applicable to a wider range of physical problems including the problems which are singular in nature. This is possible due to off-step discretization employed in the spline technique. We examine the absolute stability and super-stability of the method when applied to a problem of physical significances. We have shown that the method is absolutely stable in the case of graded mesh and super stable in the case of constant mesh. The advantage of our method lies in it being highly cost and time effective, as we employ a three-point compact stencil, thereby reducing the algebraic calculations considerably. The proposed method which is applicable to singular, boundary layer and singularly perturbed problems is a research gap which we overcame by proposing this new compact spline method.http://www.sciencedirect.com/science/article/pii/S2215016123003059Non-polynomial Spline Method for Nonlinear IVPs on a Variable Mesh. |
| spellingShingle | R.K. Mohanty Bishnu Pada Ghosh Spline-in-compression approximation of order of accuracy three (four) for second order non-linear IVPs on a graded mesh MethodsX Non-polynomial Spline Method for Nonlinear IVPs on a Variable Mesh. |
| title | Spline-in-compression approximation of order of accuracy three (four) for second order non-linear IVPs on a graded mesh |
| title_full | Spline-in-compression approximation of order of accuracy three (four) for second order non-linear IVPs on a graded mesh |
| title_fullStr | Spline-in-compression approximation of order of accuracy three (four) for second order non-linear IVPs on a graded mesh |
| title_full_unstemmed | Spline-in-compression approximation of order of accuracy three (four) for second order non-linear IVPs on a graded mesh |
| title_short | Spline-in-compression approximation of order of accuracy three (four) for second order non-linear IVPs on a graded mesh |
| title_sort | spline in compression approximation of order of accuracy three four for second order non linear ivps on a graded mesh |
| topic | Non-polynomial Spline Method for Nonlinear IVPs on a Variable Mesh. |
| url | http://www.sciencedirect.com/science/article/pii/S2215016123003059 |
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