We discuss possibilities of application of Numerical Analysis methods to proving computability, in the sense of the TTE approach, of solution operators of boundaryvalue problems for systems of PDEs. We prove computability of the solution operator for a symmetric hyperbolic system with computable real coefficients and dissipative boundary conditions, and of the Cauchy problem for the same system...

In this paper, a spline finite element approach is manipulated for the numerical solution of an extended system of second-order boundaryvalue problems. The efficiency of the proposed method is examined by comparing the results with the existing exact closed form solution. The numerical results demonstrate that the method is efficient and quite accurate when contrasted with other methods and req...

It is suggested here that an interesting and important line of inquiry is the elaboration of methods of inverse scattering transform (IST) type in contexts where non-homogeneous boundary conditions intercede. The issue, which has practical relevance we indicate by example, appears ripe for development, thanks to recent new ideas interjected into the panoply of IST methodologies. A sketch of the...

This is the abstract. The problem of statement of SaintVenant’s Principle is concerned. Statement of Boussinesq or Love is ambiguous so that its interpretations are in contradiction with each other. Rationalized Statement of SaintVenants Principle of elasticity is suggested to rule out the ambiguity of Statements of Boussinesq and Love. Rational Saint-Venant’s Principle is suggested to fit and ...

Abstract. We develop a calculus for nonlocal operators that mimics Gauss’ theorem and the Green’s identities of the classical vector calculus. The operators we define do not involve the derivatives. We then apply the nonlocal calculus to define variational formulations of nonlocal “boundaryvalue” problems that mimic the Dirichlet and Neumann problems for second-order scalar elliptic partial dif...

An analytical version of the discrete ordinates method is used to solve a class of boundaryvalue problems based on a linear Boltzmann equation relevant to the transport of neutral hydrogen atoms in a hydrogen plasma. In addition to a complete development of the discrete ordinates method for the considered application, the computational algorithm is implemented to yield very accurate results for...

A nonlinear two-dimensional theory is developed for thin magnetoelastic films capable of large deformations. This is derived directly from the three-dimensional theory. Significant simplifications emerge in the descent from three dimensions to two, permitting the self field generated by the body to be computed a posteriori. The model is specialized to isotropic elastomers and numerical solution...

Macro-elements of arbitrary smoothness are constructed on Powell-Sabin triangle splits. These elements are useful for solving boundaryvalue problems and for interpolation of Hermite data. It is shown that they are optimal with respect to spline degree, and we believe they are also optimal with respect to the number of degrees of freedom. The construction provides local bases for certain supersp...