By adding a suitable real function on both sides of the quadratic Riccati differential equation, we propose a weighted type of Adams-Bashforth rules for solving it, in which moments are used instead of the constant coefficients of Adams-Bashforth rules. Numerical results reveal that the proposed method is efficient and can be applied for other nonlinear problems.

In the present work, we have obtained the equation of state for neutron star matter considering the in uence of the ferromagnetic and antiferromagnetic spin state. We have also investigated the structure of neutron stars. According to our results, the spin asymmetry stiens the equation of state and leads to high mass for the neutron star.

We consider a fractional program with both linear and quadratic equation in numerator and denominator  having second order cone (SOC) constraints. With a suitable change of variable, we transform the problem into a  second order cone programming (SOCP)  problem.  For the quadratic fractional case, using a relaxation, the problem is reduced to a semi-definite optimization (SDO) program. The p...

Max-plus methods have been explored for solution of first-order, nonlinear HamiltonJacobi-Bellman partial differential equations (HJB PDEs) and corresponding nonlinear control problems. These methods exploit the max-plus linearity of the associated semigroups. In particular, although the problems are nonlinear, the semigroups are linear in the max-plus sense. These methods have been used succes...

This paper presents an interactive mathematical tutor application to assist middle school students with solving single-variable linear and quadratic equations and two-variable systems of linear equations. The system uses a gestural, pen-based interface to mimic and enhance the traditional step-by-step method of solving algebraic problems on paper. After the student handwrites each step, the sys...

The occurrence of SH wave propagation under the effect of a point source in an orthotropic substratum lying over a heterogeneous orthotropic half space is deliberated in the prospect of a devastating earthquake. The quadratic alteration is acknowledged for density and shear modulus which is hypothesized to be a function of depth. The method of Green's function and transformation technique contr...

By simply transforming the quadratic matrix equation into an equivalent fixed-point equation, we construct a successive approximation method and a Newton’s method based on this fixed-point equation. Under suitable conditions, we prove the local convergence of these two methods, as well as the linear convergence speed of the successive approximation method and the quadratic convergence speed of ...

In this paper we analyse the algebraic properties over the field GF(2) of the addition modulo 2. We look at implicit quadratic equations describing this operation, and at probabilistic conditional linear equations. We show that the addition modulo 2 can be partly or totally linearized when the output is fixed, and this for a large family of outputs. We apply these results to analyse the resista...

in this study we produced a new method for solving regular dierential equations with step size h and taylor series. this method analyzes a regular dierential equation with initial values and step size h. this types of equations include quadratic and cubic homogenous equations with constant coecients and cubic and second- level equations.