Numerical Methods For Ordinary Differential Equations

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:

    The moment a mere numerical superiority by either states or voters in this country proceeds to ignore the needs and desires of the minority, and for their own selfish purpose or advancement, hamper or oppress that minority, or debar them in any way from equal privileges and equal rights—that moment will mark the failure of our constitutional system.
    Franklin D. Roosevelt (1882–1945)

    There are souls that are incurable and lost to the rest of society. Deprive them of one means of folly, they will invent ten thousand others. They will create subtler, wilder methods, methods that are absolutely DESPERATE. Nature herself is fundamentally antisocial, it is only by a usurpation of powers that the organized body of society opposes the natural inclination of humanity.
    Antonin Artaud (1896–1948)

    Even in ordinary speech we call a person unreasonable whose outlook is narrow, who is conscious of one thing only at a time, and who is consequently the prey of his own caprice, whilst we describe a person as reasonable whose outlook is comprehensive, who is capable of looking at more than one side of a question and of grasping a number of details as parts of a whole.
    G. Dawes Hicks (1862–1941)

    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 (1896–1948)