Learn 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)
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)
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)