In this paper, we propose a non-polynomial spline based method to develop a numerical method for approximation to the Burgers ’ equation. Applying the Von-Neumann stability analysis, we show that the proposed method is unconditionally stable. A numerical example is given to illustrate the applicability and the accuracy of the presented new method.

The map H → H↓ assigns to each finite-dimensional space of smooth functions a homogeneous polynomial space of the same dimension. We discuss applications of this map in the areas of multivariate polynomial interpolation, box spline theory and polynomial ideals. §

We establish rigorously the fundamental nesting behavior of T-spline spaces in terms of the topology of the T-mesh. This provides a theoretical foundation for local refinement algorithms based on analysis-suitable T-splines and their use in isogeometric analysis. A key result is a dimension formula for smooth polynomial spline spaces defined over the Bézier mesh of a T-spline.

Published 1. End Conditions for Interpolatory Septic Spline Ghazala Akram and Shahid S. Siddiqi, International Journal of Computer Mathematics, Vol. 82, No. 12, 2005 pp15251540. 2. Solutions of Fifth Order Boundary-Value Problems Using NonPolynomial Spline Technique Shahid S. Siddiqi and Ghazala Akram, Applied Mathematics and Computation Vol. 175, No. 2, 2006 pp. 1574-1581. 3. Solutions of Sixt...

We derive new trace inequalities for NURBS-mapped domains. In addition to Sobolev-type inequalities, we derive discrete trace inequalities for use in NURBS-based isogeometric analysis. All dependencies on shape, size, polynomial order, and the NURBS weighting function are precisely specified in our analysis, and explicit values are provided for all bounding constants appearing in our estimates....

Simplest results presented here are the stability criteria of collocation methods for the second-order Volterra integrodifferential equation (VIDE) by polynomial spline functions. The polynomial spline collocation method is stable if all eigenvalues of a matrix are in the unit disk and all eigenvalues with |λ| = 1 belong to a 1× 1 Jordan block. Also many other conditions are derived depending u...

Wave equation is one of the second order linear hyperbolic equation. Telegraph as a special case wave has interesting point to investigate in numerical view. In this paper, we consider methods for dimensional telegraph by using cubic B-spline collocation method. Collocation method solve partial differential model problem. Cubic spline interpolation an third polynomial. This polynomial interpola...

Identification of prognostic and predictive biomarkers is important for targeting treatments to patients and for the design and analysis of randomised controlled trials. Cox proportional hazards modelling is a standard method for assessing prognostic value of clinical biomarkers where time to occurrence of an event is the primary outcome of interest. An important issue in the analysis of progno...

We introduce a non-uniform subdivision algorithm that partitions the neighborhood of an extraordinary point in the ratio σ : 1 − σ, where σ ∈ (0, 1). We call σ the speed of the non-uniform subdivision and verify C continuity of the limit surface. For σ = 1/2, the Catmull-Clark limit surface is recovered. Other speeds are useful to vary the relative width of the polynomial spline rings generated...