initial value problems for Ordinary Differential Equations

initial value problems for Ordinary Differential Equations

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Ordinary Differential Equations

Problems for Ordinary Differential Equations :

There are many problems in Science and Engineering can be reduced to the problems of solving differential equations satisfying contain certain conditions.

For Example spring mass system ,resistor-capacitor and conductance circuits ,bending of beams ,chemical reaction pendulums ,simple harmonic motion (S.H.M) the motion of a rotating mass and so on.Using analytical methods .                                                                                                        we can solve only standard types of differential equations.But the differential equation appearing in practical problems of engineering and science are not of the standard types and are complex.So ,it is rather impossible to find closed form solutions .                                                  Such equations are solved by numerical methods where the solution is given as a label of values of the function at the various values of the independent variable .this is called Point wise solution.                                                Such methods are called Point wise methods or step methods because they use y⏾n at x=x⏾n to find Yn+1 at x=x⏾n.We shall consider some of the methods commonly used to solve differential equations.

Such methods are called Point wise methods or step methods because they use y⏾n at x=x⏾n to find Yn+1 at x=x⏾n.We shall consider some of the methods commonly used to solve differential equations.