Revision as of 15:35, 1 November 2014 edit Michael Hardy (talk \| contribs) Administrators 210,577 edits →See also ← Previous edit		Revision as of 15:35, 1 November 2014 edit undo Michael Hardy (talk \| contribs) Administrators 210,577 edits →Illustration using the forward and backward Euler methods Next edit →
Line 15: : <math>\frac{dy}{dt} = -y^2, \ t\in [0, a]\quad \quad (2)</math> with the initial condition <math>y(0)=1.</math> Consider a grid <math>t_k=a\frac{k}{n}</math> for 0≤0 ≤ ''k'' ≤ ''n'', that is, the time step is <math>\Delta t=a/n,</math> and denote <math>y_k=y(t_k)</math> for each <math>k</math>. [[Discretization\|Discretize]] this equation using the simplest explicit and implicit methods, which are the ''forward Euler'' and ''backward Euler '' methods (see [[numerical ordinary differential equations]]) and compare the obtained schemes. ;Forward Euler method:

Explicit and implicit methods: Difference between revisions