This monograph is devoted to the construction of highly accurate difference schemes for parabolic boundary value problems, based on Pade approximations. The investigation is based on a new notion of positivity of difference operators in Banach spaces, which allows one to deal with difference schemes of arbitrary order of accuracy. Establishing coercivity inequalities allows one to obtain sharp - that is, two-sided - estimates of convergence rates. The proofs are based on results in interpolation theory of linear operators. The book should be of value to professional mathematicians, as well as...

A well-known and widely applied method of approximating the solutions of problems in mathematical physics is the method of difference schemes. Modern computers allow the implementation of highly accurate ones; hence, their construction and investigation for various boundary value problems in mathematical physics is generating much current interest. The present monograph is devoted to the construction of highly accurate difference schemes for parabolic boundary value problems, based on Pade approximations. The investigation is based on a new notion of positivity of difference operators in...