Solving Differential Equations:One step Methods
A lot of problems in science and engineering involve solving differential equations pendulums, RLC circuits, diffusion and so on. An ordinary differential equation can be expressed as:
Here 'phi' is the increment function or slope and h is the step size. Thus, an estimate of slope is used to extrapolate the new value y(i+1) when the previous value y(i) is known, over a distance h. The methods which are based on above equation are called one step methods. They all only differ by the definition of increment function.
Calculate y(2) for in the interval t=[0,2]. Given y(0)=1, for
Consider h=1, here
Using Euler Method: