SymbolicNMPC/MapleCodeGenerator

maple code correction

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restart;
with(plots);
with(PDEtools);
A := 1;
L := 10;
BB := 1;
f := x -> Asin(Pix/L);
PDE2 := diff(u(x, t), x $ 3) - diff(u(x, t), x)^2 + u(x, t)diff(u(x, t), x $ 2) + BB^2 - tdiff(u(x, t), x)diff(diff(u(x, t), x), t) + tdiff(u(x, t), t)*diff(u(x, t), x $ 2) = 0;
IC := u(x, 0) = f(x);
BC := {u(0, t) = 0, D1(0, t) = 1, D1(10, t) = BB};
pds := pdsolve(PDE2, {BC, IC}, numeric, time = t, range = 0 .. 10, spacestep = 0.1, timestep = 0.01);
if type(pds, 'procedure') then
plot3d(eval(u(x, t), pds), x = 0 .. 10, t = 0 .. 10, axes = boxed, labels = ["x", "t", "u(x,t)"], title = "Solution of the PDE");
else
print("Numerical solution could not be obtained.");
end if;
[animate, animate3d, animatecurve, arrow, changecoords,

complexplot, complexplot3d, conformal, conformal3d,

contourplot, contourplot3d, coordplot, coordplot3d,

densityplot, display, dualaxisplot, fieldplot, fieldplot3d,

gradplot, gradplot3d, implicitplot, implicitplot3d, inequal,

interactive, interactiveparams, intersectplot, listcontplot,

listcontplot3d, listdensityplot, listplot, listplot3d,

loglogplot, logplot, matrixplot, multiple, odeplot, pareto,

plotcompare, pointplot, pointplot3d, polarplot, polygonplot,

polygonplot3d, polyhedra_supported, polyhedraplot, rootlocus,

semilogplot, setcolors, setoptions, setoptions3d, shadebetween,

spacecurve, sparsematrixplot, surfdata, textplot, textplot3d,

tubeplot]

[CanonicalCoordinates, ChangeSymmetry, CharacteristicQ,

CharacteristicQInvariants, ConservedCurrentTest,

ConservedCurrents, ConsistencyTest, D_Dx, DeterminingPDE,

Eta_k, Euler, FirstIntegralSolver, FromJet,

FunctionFieldSolutions, InfinitesimalGenerator, Infinitesimals,

IntegratingFactorTest, IntegratingFactors, InvariantEquation,

InvariantSolutions, InvariantTransformation, Invariants,

Laplace, Library, PDEplot, PolynomialSolutions, ReducedForm,

SimilaritySolutions, SimilarityTransformation, Solve,

SymmetryCommutator, SymmetryGauge, SymmetrySolutions,

SymmetryTest, SymmetryTransformation, TWSolutions, ToJet,

ToMissingDependentVariable, build, casesplit, charstrip,

dchange, dcoeffs, declare, diff_table, difforder, dpolyform,

dsubs, mapde, separability, splitstrip, splitsys, undeclare]

                         A := 1

                        L := 10

                        BB := 1

f := proc (x) options operator, arrow; Asin(Pix/L) end proc

    /  3         \                2           /  2         \
    | d          |   / d         \            | d          |

PDE2 := |---- u(x, t)| - |--- u(x, t)| + u(x, t) |---- u(x, t)|
| 3 | \ dx / | 2 |
\ dx / \ dx /

                     /   2          \
       / d         \ |  d           |
  • 1 - t |--- u(x, t)| |------ u(x, t)|
    \ dx / \ dx dt /

                /  2         \    
    

    / d \ | d |

  • t |--- u(x, t)| |---- u(x, t)| = 0
    \ dt / | 2 |
    \ dx /

                                /1      \
             IC := u(x, 0) = sin|-- Pi x|
                                \10     /
    

BC := {u(0, t) = 0, D1(0, t) = 1, D1(10, t) = 1}

Error, (in pdsolve/numeric/process_IBCs) invalid initial/boundary condition: {u(0,t) = 0, D1(0,t) = 1, D1(10,t) = 1}
"Numerical solution could not be obtained."

NULL;