No abstract

In this paper, we derive an algorithm to solve the linear quadratic (LQ) optimal regulator problems. The new approach is based on efficient Legendre and Chebyshev formulae at the Chebyshev–Gauss–Lobatto points. The technique enjoys advantages of both the Legendre and Chebyshev approximations near the end points. To show the numerical behavior of the proposed method, the simulation results of an example are presented.

<abstract><p>We study a class of initial value problems for impulsive nonlinear wave equations. A new topological approach is applied to prove the existence of at least one and at least two nonnegative classical solutions. To prove our main results we give a suitable integral representation of the solutions of the considered problem. Then, we construct two operators so that any fixed point of their sum is a solution.</p></abstract>