Could someone explain midpoint method to me?












0












$begingroup$


I have an exercise here, but I would like to familiarise myself with the midpoint differential equation method and solve this exercise, could anyone help me out? How do I go about solving it?




Consider the ordinary differential equation initial value problem given by
$$
y'(t) = y^2 + t quad text{with} quad y(0) = 1,
$$
where $y'(t)$ denotes the time derivative of $y$.



Approximate the solution of this problem using two steps of the midpoint method
using a value of $dt = 0.2$.







ordinary-differential-equations numerical-methods







share|cite|improve this question











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  • 5




    $begingroup$
    Does the task demand the explicit midpoint method or the implicit variant? Did you find the wikipedia page for it, and what is not clear from it?
    $endgroup$
    – LutzL
    Jan 23 at 19:24


















0












$begingroup$


I have an exercise here, but I would like to familiarise myself with the midpoint differential equation method and solve this exercise, could anyone help me out? How do I go about solving it?




Consider the ordinary differential equation initial value problem given by
$$
y'(t) = y^2 + t quad text{with} quad y(0) = 1,
$$
where $y'(t)$ denotes the time derivative of $y$.



Approximate the solution of this problem using two steps of the midpoint method
using a value of $dt = 0.2$.







ordinary-differential-equations numerical-methods







share|cite|improve this question











$endgroup$








  • 5




    $begingroup$
    Does the task demand the explicit midpoint method or the implicit variant? Did you find the wikipedia page for it, and what is not clear from it?
    $endgroup$
    – LutzL
    Jan 23 at 19:24
















0












0








0





$begingroup$


I have an exercise here, but I would like to familiarise myself with the midpoint differential equation method and solve this exercise, could anyone help me out? How do I go about solving it?




Consider the ordinary differential equation initial value problem given by
$$
y'(t) = y^2 + t quad text{with} quad y(0) = 1,
$$
where $y'(t)$ denotes the time derivative of $y$.



Approximate the solution of this problem using two steps of the midpoint method
using a value of $dt = 0.2$.







ordinary-differential-equations numerical-methods







share|cite|improve this question











$endgroup$




I have an exercise here, but I would like to familiarise myself with the midpoint differential equation method and solve this exercise, could anyone help me out? How do I go about solving it?




Consider the ordinary differential equation initial value problem given by
$$
y'(t) = y^2 + t quad text{with} quad y(0) = 1,
$$
where $y'(t)$ denotes the time derivative of $y$.



Approximate the solution of this problem using two steps of the midpoint method
using a value of $dt = 0.2$.







ordinary-differential-equations numerical-methods




ordinary-differential-equations numerical-methods






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Jan 23 at 19:24









LutzL

59.6k42057




59.6k42057










asked Jan 23 at 19:06









ValVal

83




83








  • 5




    $begingroup$
    Does the task demand the explicit midpoint method or the implicit variant? Did you find the wikipedia page for it, and what is not clear from it?
    $endgroup$
    – LutzL
    Jan 23 at 19:24
















  • 5




    $begingroup$
    Does the task demand the explicit midpoint method or the implicit variant? Did you find the wikipedia page for it, and what is not clear from it?
    $endgroup$
    – LutzL
    Jan 23 at 19:24










5




5




$begingroup$
Does the task demand the explicit midpoint method or the implicit variant? Did you find the wikipedia page for it, and what is not clear from it?
$endgroup$
– LutzL
Jan 23 at 19:24






$begingroup$
Does the task demand the explicit midpoint method or the implicit variant? Did you find the wikipedia page for it, and what is not clear from it?
$endgroup$
– LutzL
Jan 23 at 19:24












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