A kind of generalized quadrature formulae of maximal degree of precision for numerical integration of analytic functions is considered. Precisely, a general weighted quadrature of Birkhoff-Young type with 4n+3 nodes and degree of precision 6n+5 is studied. Its nodes are characterized by an orthogonality relation and a general numerical method for their computation is given. Special cases and nu...

The existence and uniqueness of the Gaussian interval quadrature formula with respect to the Hermite weight function on R is proved. Similar results have been recently obtained for the Jacobi weight on [−1, 1] and for the generalized Laguerre weight on [0,+∞). Numerical construction of the Gauss–Hermite interval quadrature rule is also investigated, and a suitable algorithm is proposed. A few n...

In this paper, we interpret a fuzzy differential equation by using the strongly generalized differentiability concept. Utilizing the Generalized characterization Theorem. Then a novel hybrid method based on learning algorithm of fuzzy neural network for the solution of differential equation with fuzzy initial value is presented. Here neural network is considered as a part of large eld called ne...

The differential quadrature method (DQM) is one of the most elegant and useful approximate methods for solving initial and/or boundary value problems. It is easy to use and also straightforward to implement. However, the conventional DQM is well-known to have some difficulty in implementing multiple initial and/or boundary conditions at a given discrete point. To overcome this difficulty, this ...

Gauss quadrature rules associated with a nonnegative measure support on (part of) the real axis find many applications in Scientific Computing. It is important to be able estimate error when replacing an integral by ℓ-node rule order choose suitable number of nodes. A classical approach this evaluate (2ℓ+1)-node Gauss–Kronrod rule. However, 2ℓ+1 nodes might not exist. The generalized averaged f...

This paper describes the design and optimization of voltage controlled oscillators with quadrature outputs. Systematic design of fully integrated LC-VCOs with a high inductance tank leads to a cross-coupled double core LC-VCO as the optimal solution in terms of power consumption. Futhermore, a novel fully differential frequency tuning concept is introduced to ease high integration. The concepts...