Spline methods provide an important tool to solve singularly perturbed boundary value problems. The present paper gives a comprehensive review of computational methods based on splines used in the solution of various classes of singularly perturbed problems such as self adjoint, linear, non-linear, semi-linear, quasi-linear, singular, single parameter and multi parameter. The spline based numer...

We present a sixth-order non-polynomial spline method for the solutions of two-point nonlinear boundary value problem u(4)+f(x,u)=0, u(a)=α1, u''(a)= α2, u(b)= β1,u''(b)= β2, in off step points. Numerical method of sixth-order with end conditions of the order 6 is derived. The convergence analysis of the method has been discussed. Numerical examples are presented to illustrate the applications ...

The non-polynomial spline method is proposed to solve a singular boundary value problems. Some model problems are solved and the numerical results are compared with B-spline approximation and the exact solution. Results obtained by the method indicate the method is simple and effective. Key–Words: Singular point; Singular two-point boundary value problems; Cubic spline

An efficient method for the smooth estimation of the arrival rate of non-homogeneous, multi-dimensional Poisson processes from inexact arrivals is presented. The method provides a piecewise polynomial spline estimator using sum of squares polynomial optimization. It is easily parallelized exploiting the sparsity of the neighborhood structure of the underlying spline space; as a result, it is ve...

Non-polynomial spline is used for solution of the tenth-order linear boundary value problems. We obtained the classes of numerical methods for a specific choice of the parameters involved in non-polynomial spline. The end conditions consistent with the boundary value problems are derived. Truncation errors are given. A new approach convergence analysis of the presented methods is discussed. Two...

We construct a polynomial spline similar to the box spline, except that we relax the condition that its knots are spaced uniformly in each direction. The recurrence relation for this spline is a generalization of the recurrence relations for the box spline and univariate B-spline. The construction generalizes to exponential-polynomial splines [5]. §