Search results
Results from the Health.Zone Content Network
The TI-89 is a graphing calculator developed by Texas Instruments in 1998. The unit features a 160×100 pixel resolution LCD and a large amount of flash memory, and includes TI's Advanced Mathematics Software. The TI-89 is one of the highest model lines in TI's calculator products, along with the TI-Nspire. In the summer of 2004, the standard ...
Differential equations. In mathematics, the power series method is used to seek a power series solution to certain differential equations. In general, such a solution assumes a power series with unknown coefficients, then substitutes that solution into the differential equation to find a recurrence relation for the coefficients.
It is the most basic explicit method for numerical integration of ordinary differential equations and is the simplest Runge–Kutta method. The Euler method is named after Leonhard Euler, who first proposed it in his book Institutionum calculi integralis (published 1768–1770). [1]
The consequence of this difference is that at every step, a system of algebraic equations has to be solved. This increases the computational cost considerably. If a method with s stages is used to solve a differential equation with m components, then the system of algebraic equations has ms components.
The same illustration for The midpoint method converges faster than the Euler method, as . Numerical methods for ordinary differential equations are methods used to find numerical approximations to the solutions of ordinary differential equations (ODEs). Their use is also known as "numerical integration", although this term can also refer to ...
An ordinary differential equation ( ODE) is an equation containing an unknown function of one real or complex variable x, its derivatives, and some given functions of x. The unknown function is generally represented by a variable (often denoted y ), which, therefore, depends on x. Thus x is often called the independent variable of the equation.
The study of these differential equations with constant coefficients dates back to Leonhard Euler, who introduced the exponential function e x, which is the unique solution of the equation f′ = f such that f(0) = 1. It follows that the n th derivative of e cx is c n e cx, and this allows solving homogeneous linear differential equations ...
Almost all differential equations will have many solutions, and each constant represents the unique solution of a well-posed initial value problem. An additional justification comes from abstract algebra. The space of all (suitable) real-valued functions on the real numbers is a vector space, and the differential operator is a linear operator.