aaronkokchihan

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These are questions asked by aaronkokchihan

The following is the PDE I need to solve.

(x*y+1)*(diff(h(x, y), y, y, y))+(x+h(x, y))*(diff(h(x, y), y, y))-(diff(h(x, y), y))^2+k(x, y) = 0, (10.*(x*y+1))*(diff(k(x, y), y,y))+(10.*x+h(x,y))*(diff(k(x, y), y))-(diff(h(x, y), y))*k(x, y) = 0

 

This is the original boundary condition:

h(0, y) = f(y), h(x, 0) = 0, k(0, y) = g(y), k(x, 0) = 1, k(x, 25) = 0, (D[2](h))(x, 0) = 0, (D[2](h))(x, 25) = 0

 

After using pdsolve it come out the error:

pdsolve(eval(pde2, P = .1), pdebc4, numeric, [h(x, y), k(x, y)], spacestep = .1)

Error, (in pdsolve/numeric/par_hyp) Incorrect number of initial conditions, expected 0, got 2

 

If I remove one of the boundary condition when x=0, maybe h(0,y)=f(y), then the error will be this:

Error, (in pdsolve/numeric/par_hyp) Incorrect number of initial conditions, expected 0, got 1

 

However if I remove both when x=0, it come out this error:

Error, (in pdsolve/numeric) initial/boundary conditions must be defined at one or two points for each independent variable

 

May I know what is the problem of this equations?

P/S: I know its only differentiate with respect to y and is consider to be an ODE( I need more explantion on this please) and I'm still new to maple. Thanks!!

 

Hi,

 

I have a problem of having a problem to solve the following equation with the this error. I found out that it might be due to that I have a differential that is squared and maple could not calculate it as after square root it will have positive and negative. May I know how to overcome this other than changing my equations?

ODE_summarize.mw
 

restart; with(DEtools)

````

sol1 := alpha*(diff(f(y), y, y, y)) = -(1/4)*f(y)*(diff(f(y), y, y))*n+(1/2)*(diff(f(y), y))^2*n-(3/4)*f(y)*(diff(f(y), y, y))+(1/2)*(diff(f(y), y))^2-g(y), diff(g(y), y, y) = -(1/4)*P[r](f(y)*(diff(g(y), y))*n-4*n*(diff(f(y), y))*g(y)+3*f(y)*(diff(g(y), y)))

alpha*(diff(diff(diff(f(y), y), y), y)) = -(1/4)*f(y)*(diff(diff(f(y), y), y))*n+(1/2)*(diff(f(y), y))^2*n-(3/4)*f(y)*(diff(diff(f(y), y), y))+(1/2)*(diff(f(y), y))^2-g(y), diff(diff(g(y), y), y) = -(1/4)*P[r](f(y)*(diff(g(y), y))*n-4*n*(diff(f(y), y))*g(y)+3*f(y)*(diff(g(y), y)))

(1)

bc := (D(f))(y)

(D(f))(y)

(2)

gg := convert(bc, diff)

diff(f(y), y)

(3)

gg1 := limit(gg, y = infinity)

limit(diff(f(y), y), y = infinity)

(4)

gg2 := convert(gg1, D) = 0

limit((D(f))(y), y = infinity) = 0

(5)

gg2

(D(f))(y) = 0

(6)

bc1 := eval(f(y), y = 0) = 0, eval((D(f))(y), y = 0) = 0, convert(gg1, D) = 0, limit(g(y), y = infinity) = 0, eval(g(y), y = 0) = 1

f(0) = 0, (D(f))(0) = 0, limit((D(f))(y), y = infinity) = 0, limit(g(y), y = infinity) = 0, g(0) = 1

(7)

``

odesub1 := eval(eval(sol1, n = .6), P[r] = 0)

alpha*(diff(diff(diff(f(y), y), y), y)) = -.9000000000*f(y)*(diff(diff(f(y), y), y))+.8000000000*(diff(f(y), y))^2-g(y), diff(diff(g(y), y), y) = 0

(8)

sol2 := dsolve({bc1, odesub1}, numeric, [f(y), g(y)], output = operator, continuation = alpha, initmesh = 2400, method = bvp[midrich])

Error, (in dsolve/numeric/bvp/convertsys) unable to convert to an explicit first-order system

 

``


 

 

 

 

 

 

 

 

 

 

Hi I am new to Maple. I have 2 question:

1)I tried to run the following but I get this error as shown.pde1 is the PDE system. IBC, or you can refer bc1 to bc5 are the boundary condition given.

2)My bc4 & bc5 is suppose to be approaching 0 when y approch infinity  which is why I just put y to be equal to a large value while bc4 and bc5 equal 0. Do Maple have a function to use the approach method?

 

restart; with(PDEtools):

pde1 := [(x*y+1)*(diff(f(x, y), y, y, y))+(x+f(x, y))*(diff(f(x, y), y, y))-(diff(f(x, y), y))^2+g(x, y) = 0, (x*y+1)*(diff(g(x, y), y, y))+(x+f(x, y))*(diff(g(x, y), y))-(diff(f(x, y), y))*g(x, y) = 0];

IBC := [eval(f(x, y), y = 0) = 0, eval((D[2](f))(x, y), y = 0) = 0, eval(g(x, y), y = 0) = 0, eval((D[2](f))(x, y), y = 10000000000) = 0, eval(g(x, y), y = 10000000000) = 0];

bc1 := eval(f(x, y), y = 0) = 0

bc2 := eval((D[2](f))(x, y), y = 0) = 0

bc3 := eval(g(x, y), y = 0) = 0

bc4 := eval((D[2](f))(x, y), y = 10^10) = 0

bc5 := eval(g(x, y), y = 10^10) = 0

sol1 := pdsolve(pde1, [IBC], numeric, [f(x, y), g(x, y)], 'spacestep' = 0.1e-2, 'indepvars' = [x, y])

Error, (in pdsolve/numeric/process_IBCs) invalid initial/boundary condition: [f(x, 0) = 0, (D[2](f))(x, 0) = 0, g(x, 0) = 0, (D[2](f))(x, 1000000000000) = 0, g(x, 1000000000000) = 0]

Thanks you in advance.

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