Adaptive Solution of Partial Differential Equations in Multiwavelet Bases B. Alpert,∗,1 G. Beylkin,†,2 D. Gines,† and L. Vozovoi‡,3,4,5 ∗National Institute of Standards and Technology, Boulder, Colorado 80305-3328; †Department of Applied Mathematics, University of Colorado, Boulder, Colorado 80309-0526; and ‡School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel E-mail: al...

a computational method for numerical solution of a nonlinear volterra and fredholm integro-differentialequations of fractional order based on chebyshev cardinal functions is introduced. the chebyshev cardinaloperational matrix of fractional derivative is derived and used to transform the main equation to a system ofalgebraic equations. some examples are included to demonstrate the validity and ...

Model generation has emergcd as a key task in engineering design and analysis. Al research in this area has focusedon model based reasoning emphasising qualitative models in attempting to automate this process. In this paper, we propose that this work on the use of model based reasoning in model generation would benefit from the inclusion of case-based reasoning (CBR) techniques. We argue that ...

with x0 ∈ R, B ∈ R and E,A ∈ R, such that the pencil sE − A ∈ R[s] is regular, that is, det(sE −A) 6= 0. For systems governed by ordinary differentialequations (that is, E is the identity matrix), a rigorous analysis of this problem has its origin in the 60s of the 20th century [6, 8–10, 13, 15, 21]. In particular, the article [20] by Willems gives a complete characterization of linear-quadrati...

In this paper, an elastic shell model is presented for postbuckling prediction of a long thinwalledcylindrical shell under axial compression. The Ritz method is applied to solve the governingequilibrium equation of a cylindrical shell model based on the von-Karman type nonlinear differentialequations. The postbuckling equilibrium path is obtained using the energy method for a long thin-walledcy...