The use of cubic splines in the numerical solution of a system of second-order boundary value problems

Exponential spline solutions for a class of two point boundary value problems over a semi-infinite range

“…• For (α, β) = 1 24 (1, 22) the scheme (2.9) reduces to cubic polynomial spline scheme. (See [2]). Then local truncation errors in (2.9) for these two cases is:…”

“…Consider the boundary value problem −y (2) The analytical solution of (6.1) with one of the boundary conditions given by Eqns (6.2-6.5) is…”

“…We consider the following second order differential equation over a semiinfinite range: The numerical analysis literature contains little for finding an approximate solution of this problem with one of the boundary conditions (1.2-1.5) while there is a lot of numerical methods treated this problem with Dirichlet and Neumann boundary conditions for example see [1,2,[4][5][6][8][9][10] and references there in. Chawla and Shivakumar [3] developed a second order method based on finite difference for the boundary value problems (1.1-1.2).…”

Galerkin's finite element formulation of the system of fourth-order boundary-value problems

“…The idea (variational inequality theory) is being applied to various fields of mathematical and engineering sciences e.g., elasticity, mechanics, transportation, fluid flow through porous media, optimal control and structural analysis, etc. [1][2][3][4][5][6][7]. An important foundation for the applications of variational inequalities is provided by the contact problems.…”

“…In recent years, some finite difference and quintic spline methods have developed by Al-Said and Noor [1,2] and Noor and Al-Said [8,9] for solving fourth order system of differential equations associated with obstacle and unilateral problems. Khalifa and Noor [5,10] discussed the possibility of using collocation method with quintic splines as basis functions for obstacle problems.…”