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- Mladen Rogina
- 2006

We show that it is possible to construct stable, explicit finite difference approximations for the classical solution of the initial value problem for the parabolic systems of the form ∂ t u = A(t, x)u + f on R d , where A(t, x) = ij a ij (t, x)∂ i ∂ j + i b i (t, x)∂ i + c(t, x). The numerical scheme relies on an approximation of the elliptic operator A(t,… (More)

- Ned Zad Limi, Mladen Rogina
- 2007

A class of numerical methods for ODE which are explicit, absolutely stable, and of any order of convergence, is constructed. Methods can be eeciently applied to those initial value problems for the 2 nd-order parabolic system which have solutions with nite L1-norms. Numerical procedure consists of two basic steps. The space discretizations of elliptic… (More)

- Mladen Rogina
- 2007

We describe explicitly each stage of a numerically stable algorithm for calculating with exponential tension B-splines with non-uniform choice of tension parameters. These splines are piecewisely in the kernel of D 2 (D 2 − p 2), where D stands for ordinary derivative, defined on arbitrary meshes, with a different choice of the tension parameter p on each… (More)

We consider a second order differential operator A(Ü) = − d i,j=1 ∂iaij (Ü)∂j + d j=1 ∂j bj (Ü)· + c(Ü) on R d , on a bounded domain D with Dirichlet boundary conditions on ∂D, under mild assumptions on the coefficients of the diffusion tensor aij. The object is to construct monotone numerical schemes to approximate the solution of the problem A(Ü) u(Ü) =… (More)

- Tina Bosner, Mladen Rogina
- 2006

We propose a knot insertion algorithm for splines that are piecewisely in L{1, x, sin x, cos x}. Since an ECC–system on [0, 2π] in this case does not exist, we construct a CCC–system by choosing the appropriate measures in the canonical representation. In this way, a B-basis can be constructed in much the same way as for weighted and tension splines. Thus… (More)

- Mladen Rogina
- 1999

It is an important fact that general families of Cheby-shev and L-splines can be locally represented, i.e. there exists a basis of B-splines which spans the entire space. We develop a special technique to calculate with 4 th order Chebyshev splines of minimum deficiency on nonuniform meshes, which leads to a numerically stable algorithm, at least in case… (More)

Variable degree polynomial (VDP) splines have recently proved themselves as a valuable tool in obtaining shape preserving approximations. However, some usual properties which one would expect of a spline space in order to be useful in geometric modeling, do not follow easily from their definition. This includes total positivity (TP) and variation… (More)