Mladen Rogina

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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)
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)
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)
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)