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- 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)

- Miljenko Marusic, Mladen Rogina
- Adv. Comput. Math.
- 1996

We develop a technique to calculate with Chebyshev Splines of orders 3 and 4, based on the known derivative formula for Chebyshev splines and an Oslo type algorithm. We assume that splines in the reduced system are simple enough to calculate. Local bases of Chebyshev splines of order 3 and 4 can thus be evaluated as positive linear combinations of less… (More)

- Vera Culjak, Mladen Rogina
- 1999

In this paper we prove some inequalities for convex function of a higher order. The well known Hermite interpolating polynomial leads us to a converse of Jensen inequality for a regular, signed measure and, as a consequence, a generalization of Hadamard and Petrovi c's inequalities. Also, we obtain a new upper bound for the error function of the Hermite… (More)

- Tina Bosner, Mladen Rogina
- Numerical Algorithms
- 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)

- Mladen Rogina
- 1999

It is an important fact that general families of Chebyshev 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 order Chebyshev splines of minimum deficiency on nonuniform meshes, which leads to a numerically stable algorithm, at least in case one… (More)

- 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 ∂tu = A(t,x)u + f on R, where A(t,x) = ∑ ij aij(t,x)∂i∂j + ∑ i bi(t,x)∂i + c(t,x). The numerical scheme relies on an approximation of the elliptic operator A(t,x) on an… (More)

We consider a second order differential operator A( ) = − ∑d i,j=1 ∂iaij( )∂j + ∑d j=1 ∂j ( bj( )· ) +c( ) on R, 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( )u( ) =… (More)

- Mladen Rogina
- 2007

There are known methods of approximating the solution of parabolic 2 nd order systems by solving stochastic diierential equations instead. The main idea is based on the fact that stochastic diierential equation deenes a diiusion process, generated by an elliptic diierential operator on R d. We propose a diierence scheme for the ellip-tic operator, which… (More)

- Mladen Rogina, John J. H. Miller, +22 authors Vedran Novakovic
- 2009

Most of the research in the field of multiphase flows in porous media, over the past four decades, has been motivated by applications either on unsaturated groundwater flows or on underground petroleum reservoirs. Most recently, multiphase flows have generated serious interest among engineers concerned with deep geological repository for radioactive waste,… (More)