Numerical studies for solving the Logistic and Riccati Di¤erential Equation
ثبت نشده
چکیده
In this paper, we will solve the Logistic and Riccati di¤erential equations using VIM, shifted Chebyshev-spectral fourth kind methods and Hermite collocation method. Where we can from the numerical results we obtained to conclude that the solution using these three approaches converge to the exact solution is excellent. We note that we can apply the proposed methods to solve other problems in engineering and physics.
منابع مشابه
Numerical Solution of fuzzy differential equations of nth-order by Adams-Bashforth method
So far, many methods have been presented to solve the rst-order di erential equations. But, not many studies have been conducted for numerical solution of high-order fuzzy di erential equations. In this research, First, the equation by reducing time, we transform the rst-order equation. Then we have applied Adams-Bashforth multi-step methods for the initial approximation of one order di erentia...
متن کاملRational Heuristics for Rational Solutions of Riccati Equations
We describe some new algorithm and heuristics for computing the polynomial and rational solutions of bounded degree of a class of ordinary di erential equations, which includes generalized Riccati equations. As a consequence, our methods can be used for factoring linear ordinary di erential equations. Since they generate systems of algebraic equations in at most n unknowns, where n is the order...
متن کاملAn exponential spline for solving the fractional riccati differential equation
In this Article, proposes an approximation for the solution of the Riccati equation based on the use of exponential spline functions. Then the exponential spline equations are obtained and the differential equation of the fractional Riccati is discretized. The effect of performing this mathematical operation is obtained from an algebraic system of equations. To illustrate the benefits of the me...
متن کاملApplication of fractional-order Bernoulli functions for solving fractional Riccati differential equation
In this paper, a new numerical method for solving the fractional Riccati differential equation is presented. The fractional derivatives are described in the Caputo sense. The method is based upon fractional-order Bernoulli functions approximations. First, the fractional-order Bernoulli functions and their properties are presented. Then, an operational matrix of fractional order integration...
متن کاملUnconventional Reeexive Numerical Methods for Matrix Diierential Riccati Equations 1 Unconventional Reeexive Numerical Methods for Matrix Diierential Riccati Equations
Matrix Di erential Riccati Equations (MDREs) X = A21 XA11 + A22X XA12X; X(0) = X0; where Aij Aij(t), appear frequently throughout applied mathematics, science, and engineering. MDREs play particularly important roles in optimal control, ltering, estimation, and in two-point linear boundary value problems. In the past a number of unconventional numerical methods that are suited only for time-inv...
متن کامل