Review of iterative solutions to partial differential equations.

It may be useful to paste some material from here

\frac{dx}{dt}=2

\frac{x(t+\Delta t)-x(t)}{\Delta t}=2

x(t+\Delta t)= x(t)+2 \Delta t \

Now pick an initial t, say $$ t=0 $$ . Assume a boundary condition, $$ x(0)=7 $$ .

Then $x(0)=x_{0}$ , so $x_{0}=7$ .

Then $x(\Delta t)=x_{1}$ , so $x_{1}=7+\Delta t2=7.2$ (We pick $\Delta t=0.2$ )

Then $x(2\Delta t)=x_{2}$ , so $x_{2}=7.2+\Delta t2=7.4$

[Plot of solution]

Solving differential equations iteratively Old Kiwi - Rhea