Hello everyone,

I have nonlinear partial differential equations (see the attached file) need to be solved:

https://drive.google.com/file/d/0B14...ew?usp=sharing

With initial condition: h(x, y) = K1 (constant), dh/dx = K2 (constant); dh/dy = K3 (constant); And h(x,y) is function of (x,y) other factors are constant. Could anyone tell me how to solve these equations by using numerical method? Do you know any library in c/ c++ language that can solve these equations??

I have tried with Maple 17 and the response is: "Error, (in pdsolve/info) first argument is not a differential equation". Whole of my input:

**with(PDEtools); declare(U1(x, y), U2(x, y), U3(x, y));**

**PDEs = [diff(U1(x, y), y) = U2(x, y), **

**diff(U1(x, y), x) = U3(x, y), **

**(diff(U2(x, y), y))*((L-U1(x, y))^2+(D2+tan(alpha)*(L+U1(x, y)))^2)+.5*U2(x, y)*(2*tan(alpha)*U1(x, y)-D2) = 0,**

** (diff(U3(x, y), x))*((L-U1(x, y))^2+D1^2*cos(alpha+2*U2(x, y))^2)+.5*U3(x, y)*D1*cos(alpha+2*U2(x, y))+.5*D1*sin(alpha+2*U2(x, y))*(L-U1(x, y)) = 0];**

[ d d / d

PDEs = [--- U1(x, y) = U2(x, y), --- U1(x, y) = U3(x, y), |--- U2(

[ dy dx \ dy

\ / 2 2\

x, y)| \(L - U1(x, y)) + (D2 + tan(alpha) (L + U1(x, y))) /

/

/ d

+ 0.5 U2(x, y) (2 tan(alpha) U1(x, y) - D2) = 0, |--- U3(x, y)

\ dx

\ / 2 2 2\

| \(L - U1(x, y)) + D1 cos(alpha + 2 U2(x, y)) /

/

+ 0.5 U3(x, y) D1 cos(alpha + 2 U2(x, y))

]

+ 0.5 D1 sin(alpha + 2 U2(x, y)) (L - U1(x, y)) = 0]

]

**pdsolve(PDEs);**

Error, (in pdsolve/info) first argument is not a differential equation

I will be very appreciated with your help!!!