This study deals with the numerical solution of a class linear systems second-order boundary value problems (BVPs) using new symmetric cubic B-spline method (NCBM). is typical collocation powered by approximations for derivatives. The flexibility and high order precision functions allow them to approximate answers. These have symmetrical property. approximation plays an important role in produc...

It is well known that fourth-order boundary value problems (BVPs) arise in a variety of different areas of the flexibility mechanics and engineering physics and thus have been extensively studied; for instance, see [1–29] and references therein. Boundary value problems with integral boundary conditions appear in heat conduction, thermoelasticity, chemical engineering underground water flow, and...

where n ≥ , f : [, ]× (R+)n– → R+ is continuous in which R+ = [,+∞), A and B are right continuous on [, ), left continuous at t = , and nondecreasing on [, ], withA() = B() = ; ∫   v(s)dA(s) and ∫   v(s)dB(s) denote the Riemann-Stieltjes integrals of v with respect to A and B, respectively. Boundary value problems (BVPs for short) for nonlinear differential equations arise in m...

Shape gradients of PDE constrained shape functionals can be stated in two equivalent ways. Both rely on the solutions of two boundary value problems (BVPs), but one involves integrating their traces on the boundary of the domain, while the other evaluates integrals in the volume. Usually, the two BVPs can only be solved approximately, for instance, by finite element methods. However, when used ...

V. OPTICAL KERR EFFECT ........................................................................................................................... 11 • BOUND ELECTRONIC OPTICAL KERR EFFECT IN SOLIDS.................................................................................... 11 • RE-ORIENTATIONAL KERR EFFECT IN LIQUIDS ........................................................................