How to gain the exact solution of the partial discrete equation...
$begingroup$
I made a mathematical discrete model of one dimensional flow.
Then I achieved this equation:
$u(n,m+1)=u(n-1,m)+u(n,m)(u(n+1,m)-u(n-1,m))$
Where n ,m are integer and $0leq u leq 1 $ for all n, m.
Numerical experiments implies it has traveling wave solution under moderate boundary condition.I want to know its exact solution.Please tell me.
calculus discrete-mathematics recurrence-relations mathematical-modeling integrable-systems
asked Jan 16 at 1:21
Ko HeyKo Hey
12
$endgroup$
add a comment |
$begingroup$
I made a mathematical discrete model of one dimensional flow.
Then I achieved this equation:
$u(n,m+1)=u(n-1,m)+u(n,m)(u(n+1,m)-u(n-1,m))$
Where n ,m are integer and $0leq u leq 1 $ for all n, m.
Numerical experiments implies it has traveling wave solution under moderate boundary condition.I want to know its exact solution.Please tell me.
calculus discrete-mathematics recurrence-relations mathematical-modeling integrable-systems
asked Jan 16 at 1:21
Ko HeyKo Hey
12
$endgroup$
$begingroup$
I heard that Burgers' equation is pretty well studied.
$endgroup$
– Ivan Neretin
Jan 29 at 8:24
add a comment |
$begingroup$
I made a mathematical discrete model of one dimensional flow.
Then I achieved this equation:
$u(n,m+1)=u(n-1,m)+u(n,m)(u(n+1,m)-u(n-1,m))$
Where n ,m are integer and $0leq u leq 1 $ for all n, m.
Numerical experiments implies it has traveling wave solution under moderate boundary condition.I want to know its exact solution.Please tell me.
calculus discrete-mathematics recurrence-relations mathematical-modeling integrable-systems
asked Jan 16 at 1:21
Ko HeyKo Hey
12
$endgroup$
I made a mathematical discrete model of one dimensional flow.
Then I achieved this equation:
$u(n,m+1)=u(n-1,m)+u(n,m)(u(n+1,m)-u(n-1,m))$
Where n ,m are integer and $0leq u leq 1 $ for all n, m.
Numerical experiments implies it has traveling wave solution under moderate boundary condition.I want to know its exact solution.Please tell me.
calculus discrete-mathematics recurrence-relations mathematical-modeling integrable-systems
calculus discrete-mathematics recurrence-relations mathematical-modeling integrable-systems
asked Jan 16 at 1:21
Ko HeyKo Hey
12
asked Jan 16 at 1:21
Ko HeyKo Hey
12
edited Jan 29 at 8:12
Ko Hey
asked Jan 16 at 1:21
Ko HeyKo Hey
12
asked Jan 16 at 1:21
Ko HeyKo Hey
12
asked Jan 16 at 1:21
Ko HeyKo Hey
12
12
$begingroup$
I heard that Burgers' equation is pretty well studied.
$endgroup$
– Ivan Neretin
Jan 29 at 8:24
add a comment |
$begingroup$
I heard that Burgers' equation is pretty well studied.
$endgroup$
– Ivan Neretin
Jan 29 at 8:24
$begingroup$
I heard that Burgers' equation is pretty well studied.
$endgroup$
– Ivan Neretin
Jan 29 at 8:24
$begingroup$
I heard that Burgers' equation is pretty well studied.
$endgroup$
– Ivan Neretin
Jan 29 at 8:24
add a comment |
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$begingroup$
I heard that Burgers' equation is pretty well studied.
$endgroup$
– Ivan Neretin
Jan 29 at 8:24