Fill out the form below to set up a numeric solution
to your partial differential equation with boundary values.
Up to third order in four dimensions, x,y,z,t .

Title

Email results, numeric and plot

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Finite Element Method
Discrete approximation method

Uxxx denotes d^3 U(x,y,z,t)/dx^3 Uxy denotes d^2 U(x,y,z,t)/dx xy
Uz denotes d U(x,y,z,t)/dz etc. enter your values of cxxx, cxy, cz etc.
The default is zero, all 35 possible derivatives are listed.
cxxx Uxxx + cyyy Uyyy + czzz Uzzz + cttt Uttt +
cxxy Uxxy + cxxz Uxxz + cxxt Uxxt + cxyy Uxyy +
cxyz Uxyz + cxyt Uxyt + cxzz Uxzz + cxzt Uxzt +
cxtt Uxtt + cyyz Uyyz + cyyt Uyyt + cyzz Uyzz +
cyzt Uyzt + cytt Uytt + czzt Uzzt + cztt Uztt +
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)

cxxx cyyy czzz cttt

cxxy cxxz cxxt cxyy

cxyz cxyt cxzz cxzt

cxtt cyyz cyyt cyzz

cyzt cytt czzt cztt

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,t
must be valid for all y in range when x=xmax or x=xmin
must be valid for all x in range when y=ymin or y=ymax
must be valid for all z in range when z=zmax or z=zmin
must be valid for all t 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)
step 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.

xmin xmax nx

ymin ymax ny

zmin zmax nz

tmin tmax nt