Fill out the form below to set up a numeric solution
to your partial differential equation with boundary values.
Up to second order in four dimensions.

Title

Email results, numeric and plot

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Finite Element Method
Discrete approximation method

Uxx denotes d^2 U(x,y,z,t)/dx^2 Uxy denotes d^2 U(x,y,z,t)/dx dy
Ux denotes d U(x,y,z,t)/dx etc.
Enter your values of cxx, cyy, czz, ctt, etc.
Optional enter your equations in x,y,z,t for cxx, cyy, czz, ctt, etc.
Do not enter "=", ";", use "C" language math routines and syntax.

cxx Uxx + cyy Uyy + czz Uzz + ctt Utt + cxy Uxy + cxz Uxz + cxt Uxt + cyz Uyz + cyt Uyt + czt Uzt + cx Ux + cy Uy + cz Uz + ct Ut + c U = f(x,y,z,t)

cxx cyy czz ctt

cxy cxz cxt

cyz cyt czt

cx cy cz ct c


ub(x,y,z,t)=

ub(x,y,z,t) = boundary equation in x,y,z
must be valid for all y,z,t in range when x=xmax or x=xmin
must be valid for all x,z,t in range when y=ymin or y=ymax
must be valid for all x,y,t in range when z=zmin or z=zmax
must be valid for all x,y,z in range when t=tmin or t=tmax
must be legal "C" or Java, or Python, etc.

x, y, z, t, Dirichlet_boundary_value (each line)

An optional method to define the boundary is to upload a file
with a sequence of x,y,z,t,boundary_value lines that enclose the boundary
step hx=(xmax-xmin)/(nx-1), hy=(ymax-ymin)/(ny-1)
hz=(zmax-zmin)/(nz-1), ht=(tmax-tmin)/(nt-1)

f(x,y,z,t)=

f(x,y,z,t) = right hand side equation in x,y,z,t
must be legal "C" or Java, or Python, etc.

Solution range and number of points

xmin xmax nx

ymin ymax ny

zmin zmax nz

tmin tmax nt