Numerical Methods For Ordinary Differential Equations
Numerical ordinary differential equations is the part of numerical analysis which studies the numerical solution of ordinary differential equations (ODEs). This field is also known under the name numerical integration, but some people reserve this term for the computation of integrals.
Many differential equations cannot be solved analytically; however, in science and engineering, a numeric approximation to the solution is often good enough to solve a problem. The algorithms studied here can be used to compute such an approximation. An alternative method is to use techniques from calculus to obtain a series expansion of the solution.
Ordinary differential equations occur in many scientific disciplines, for instance in physics, chemistry, biology, and economics. In addition, some methods in numerical partial differential equations convert the partial differential equation into an ordinary differential equation, which must then be solved.
Read more about Numerical Methods For Ordinary Differential Equations: The Problem, Methods, Analysis, History, Numerical Solutions To Second Order One Dimensional Boundary Value Problems
Famous quotes containing the words numerical, methods, ordinary and/or differential:
“There is a genius of a nation, which is not to be found in the numerical citizens, but which characterizes the society.”
—Ralph Waldo Emerson (18031882)
“I believe in women; and in their right to their own best possibilities in every department of life. I believe that the methods of dress practiced among women are a marked hindrance to the realization of these possibilities, and should be scorned or persuaded out of society.”
—Elizabeth Stuart Phelps (18441911)
“One has often wondered whether upon the whole earth there is anything so unintelligent, so unapt to perceive how the world is really going, as an ordinary young Englishman of our upper class.”
—Matthew Arnold (18221888)
“But how is one to make a scientist understand that there is something unalterably deranged about differential calculus, quantum theory, or the obscene and so inanely liturgical ordeals of the precession of the equinoxes.”
—Antonin Artaud (18961948)