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

Title

Email results, numeric and plot

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Finite Element Method
Discrete approximation method

Uxxxx denotes d^4 U(x,y,z,t)/dx^4 Uxy denotes d^4 U(x,y,z,t)/dx^2 dy^2
Ut denotes d U(x,y,z,t)/dt etc. enter your values of cxxxx, cxxyy, ct etc.
The default is zero, all 70 possible derivatives are listed.

cxxxx Uxxxx + cyyyy Uyyyy + czzzz Uzzzz + ctttt Utttt +
cxxxy Uxxxy + cxxxz Uxxxz + cxxxt Uxxxt + cxxyy Uxxyy +
cxxyz Uxxyz + cxxyt Uxxyt + cxxzz Uxxzz + cxxzt Uxxzt +
cxxtt Uxxtt + cxyyy Uxyyy + cxyyz Uxyyz + cxyyt Uxyyt +
cxyzz Uxyzz + cxyzt Uxyzt + cxytt Uxytt + cxzzz Uxzzz +
cxzzt Uxzzt + cxztt Uxztt + cxttt Uxttt + cyyyz Uyyyz +
cyyyt Uyyyt + cyyzz Uyyzz + cyyzt Uyyzt + cyytt Uyytt +
cyzzz Uyzzz + cyzzt Uyzzt + cyztt Uyztt + cyttt Uyttt +
czzzt Uzzzt + czztt Uzztt + czttt Uzttt +
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)

cxxxx cyyyy czzzz ctttt

cxxxy cxxxz cxxxt cxxyy

cxxyz cxxyt cxxzz cxxzt

cxxtt cxyyy cxyyz cxyyt

cxyzz cxyzt cxytt cxzzz

cxzzt cxztt cxttt cyyyz

cyyyt cyyzz cyyzt cyytt

cyzzz cyzzt cyztt cyttt

czzzt czztt czttt

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