General Linear Methods for Volterra Integro-differential Equations with Memory
نویسندگان
چکیده
منابع مشابه
General Linear Methods for Volterra Integro-differential Equations with Memory
A new class of numerical methods for Volterra integro-differential equations with memory is developed. The methods are based on the combination of general linear methods with compound quadrature rules. Sufficient conditions that guarantee global and asymptotic stability of the solution of the differential equation and its numerical approximation are established. Numerical examples illustrate th...
متن کاملLinear Multistep Methods for Volterra Integral and Integro-Differential Equations
In these appendices we present, successively, I conditions for the existence of a unique solution of (1.1) and (1.2); II three tables of coefficients of forward differentiation formulas, and of two common LM formulas for ODEs, viz., backward differentiation formulas and Adams-Moulton formulas; III two lemmas which are needed in: IV proofs of the main results of this paper, as far as they are no...
متن کاملMultistep collocation methods for Volterra integro-differential equations
Keywords: Volterra integro-differential equations Multistep collocation Superconvergence Stability a b s t r a c t Multistep collocation methods for Volterra integro-differential equations are derived and analyzed. They increase the order of convergence of classical one-step collocation methods, at the same computational cost. The numerical stability analysis is carried out and classes of A 0-s...
متن کاملSplitting Methods for Partial Volterra Integro-Differential Equations
The spatial discretization of initial-boundary-value problems for (nonlinear) parabolic or hyperbolic PDEs with memory terms leads to (large) systems of Volterra integro-differential equations (VIDEs). In this paper we study the efficient numerical solution of such systems by methods based on linear multistep formulas, using special factorization (or splitting) techniques in the iterative solut...
متن کاملGeneral linear methods for Volterra integral equations
s of IWANASP, September 10 – 12, 2008, Ericeira, Portugal GENERAL LINEAR METHODS FOR VOLTERRA INTEGRAL EQUATIONS ZDZISÃlAW JACKIEWICZ Departament of Mathematics, Arizona State University Tempe, Arizona 85287, USA E-mail: [email protected] We investigate the class of general linear methods of order p and stage order q = p for the numerical solution of Volterra integral equations of the se...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: SIAM Journal on Scientific Computing
سال: 2006
ISSN: 1064-8275,1095-7197
DOI: 10.1137/040607058