Consider these code, which solve the same equation using DSolve and NDSolve, why do they give different answer? I'm using version 11.0 on Win.

Consider these code, which solve the same equation using DSolve and NDSolve, why do they give different answer? I'm using version 11.0 on Windows 8.1.

Another example:

L = 2; eq = D[u[x, t], t] == D[u[x, t], x, x]; opts = Method -> {"MethodOfLines", "SpatialDiscretization" -> {"FiniteElement", "MeshOptions" -> {"MaxCellMeasure" -> 0.001}}}; sol1 = NDSolveValue[{eq, u[x, 0] == x, u[0, t] == 1, u[2, t] == 1}, u, {x, 0, L}, {t, 0, L}, opts]; sol2 = u[x, t] /. First@DSolve[{eq, u[x, 0] == x, u[0, t] == 1, u[2, t] == 1}, u[x, t], {x, t}] (* 1 + Inactive[Sum][-(( 2 (1 + (-1)^K[1]) E^(-(1/4) \[Pi]^2 t K[1]^2) Sin[1/2 \[Pi] x K[1]])/(\[Pi] K[1])), {K[1], 1, \[Infinity]}] *) T = 1/10; Plot[{Evaluate[sol1[x, T]], Evaluate[sol2 /. {Infinity -> 100} /. t -> T // Activate]}, {x, 0, L}, PlotLegends -> {"numeric solution", "symbolic solution"}] 

Consider these code, which solve the same equation using DSolve and NDSolve, why do they give different answer? I'm using version 11.0 on Win.

eq = D[u[x, t], t] == D[u[x, t], x, x]; icsbc = {u[x, 0] == 1, u[0, t] == 0, u[1, t] == 0}; numer1 = NDSolve[{eq, icsbc}, u, {x, 0, 1}, {t, 0, 1}] numer2 = NDSolve[{eq, icsbc}, u, {x, 0, 1}, {t, 0, 1}, Method -> {"MethodOfLines", "SpatialDiscretization" -> "FiniteElement"}] numer3 = NDSolve[{eq, icsbc}, u, {x, 0, 1}, {t, 0, 1}, Method -> {"MethodOfLines", "SpatialDiscretization" -> {"TensorProductGrid", "MinPoints" -> 200}}] symbol = DSolve[{eq, icsbc}, u[x, t], {x, t}]   Plot[{Evaluate[u[x, 1/2] /. numer1], Evaluate[u[x, 1/2] /. numer2], Evaluate[u[x, 1/2] /. numer3], Evaluate[(u[x, t] /. symbol[[1]] /. t -> 1/2 /. {Infinity -> 10} // Activate)]}, {x, 0, 1}, PlotLegends -> {"numeric1", "numeric2", "numeric3", "symbolic"}, PlotStyle -> {{Green, Dashing[{0.1, 0.1}], Thin}, {Blue, Dashing[{0.05, 0.05}], Thin}, {Yellow, Dashing[{0.01, 0.01}], Thin}, {Black, Thickness[0.02]}}] 

Consider these code, which solve the same equation using DSolve and NDSolve, why do they give different answer? I'm using version 11.0 on Win.

eq = D[u[x, t], t] == D[u[x, t], x, x]; icsbc = {u[x, 0] == 1, u[0, t] == 0, u[1, t] == 0}; numer1 = NDSolve[{eq, icsbc}, u, {x, 0, 1}, {t, 0, 1}] numer2 = NDSolve[{eq, icsbc}, u, {x, 0, 1}, {t, 0, 1}, Method -> {"MethodOfLines", "SpatialDiscretization" -> "FiniteElement"}] numer3 = NDSolve[{eq, icsbc}, u, {x, 0, 1}, {t, 0, 1}, Method -> {"MethodOfLines", "SpatialDiscretization" -> {"TensorProductGrid", "MinPoints" -> 200}}] symbol = DSolve[{eq, icsbc}, u[x, t], {x, t}] 

symbol = {{u[x, t] -> Inactive[Sum][-(( 2 (-1 + (-1)^K[1]) E^(-\[Pi]^2 t K[1]^2) Sin[\[Pi] x K[1]])/(\[Pi] K[1])), {K[1], 1, \[Infinity]}]}}

Plot[{Evaluate[u[x, 1/2] /. numer1], Evaluate[u[x, 1/2] /. numer2], Evaluate[u[x, 1/2] /. numer3], Evaluate[(u[x, t] /. symbol[[1]] /. t -> 1/2 /. {Infinity -> 10} // Activate)]}, {x, 0, 1}, PlotLegends -> {"numeric1", "numeric2", "numeric3", "symbolic"}, PlotStyle -> {{Green, Dashing[{0.1, 0.1}], Thin}, {Blue, Dashing[{0.05, 0.05}], Thin}, {Yellow, Dashing[{0.01, 0.01}], Thin}, {Black, Thickness[0.02]}}]