Recent Advances in Numerical Analysis provides information pertinent to the developments in numerical analysis. This book covers a variety of topics, including positive functions, Sobolev spaces, computing paths, partial differential equations, and perturbation theory. Organized into 12 chapters, this book begins with an overview of stability conditions for numerical methods that can be expressed in the form that some associated function is positive. This text then examines the polynomial approximation theory having applications to finite element Galerkin methods. Other chapters consider the numerical condition of polynomials by examining three particular problem areas, namely, the representation of polynomials, algebraic equations, and the problem of orthogonalization. This book discusses as well a general theory that leads to a systematic way to prepare the initial data. The final chapter deals with the derivation of the Kronecker canonical form. This book is a valuable resource for applied mathematicians, numerical analysts, physicists, engineers, and research workers.Thus as the mesh is refined the code will tend to go to higher orders. ... computation the code goes to a higher order, we expect that the error will be reduced by more than a factor of 10. 8. ... of a stiff problem, meaning here that an unrealistically small step size would be necessary to solve the problem with a code like oursanbsp;...
|Title||:||Recent Advances in Numerical Analysis|
|Author||:||Carl De Boor, Gene H. Golub|
|Publisher||:||Academic Press - 2014-05-10|