Question

Does accuracy of the numerical solution of a PDE depend on the scaling of the variables?

score 88 · Answer 1 · 2026-05-10 11:21:55

88

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Does accuracy of the numerical solution of a PDE depend on the scaling of the variables?

Published on 10 May 2026 - 11:21

score 772 · Answer 2 · 2026-04-11 05:40:38

772

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Heat Equation (Partial Differential Equation) - Fourier Transform Solution Form.

Published on 11 Apr 2026 - 5:40

score 395 · Answer 3 · 2026-04-09 12:01:48

395

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Laplace transform of heat equation in spherical coordinates

Published on 09 Apr 2026 - 12:01

score 54 · Answer 4 · 2026-04-13 20:37:28

54

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Show that $u^2$ satisfies $\partial_t(u^2) = 2k[\partial_x(u\partial_xu) - (\partial_x u)^2]$

Published on 13 Apr 2026 - 20:37

score 56 · Answer 5 · 2026-04-16 13:46:26

56

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Show that the norm $N_1(t) = \int_0^L(u(x,t) - u_0)^2dx$ is monotonically decreasing in time.

Published on 16 Apr 2026 - 13:46

score 69 · Answer 6 · 2026-04-10 16:59:28

69

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How to inverse a Fourier series?

Published on 10 Apr 2026 - 16:59

score 2k · Answer 7 · 2026-04-11 22:12:04

2k

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Understanding Duhamel's principle, PDE

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score 613 · Answer 8 · 2026-04-11 22:51:26

613

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Solve heat equation with nonlinear term in matlab - Does my solution look reasonable?

Published on 11 Apr 2026 - 22:51

score 212 · Answer 9 · 2026-04-29 12:25:17

212

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Calculation/Verification of an integral kernel for $\operatorname{e}^{t\Delta}(1-\Delta)^{-\frac{1}{4}}$

Published on 29 Apr 2026 - 12:25

score 111 · Answer 10 · 2026-03-25 01:21:17

111

Views

Heat Equation with Antiperiodic BCs

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score 176 · Answer 11 · 2026-04-13 09:20:36

176

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1d PDE's on infinite Domains using fundamental solutions.

Published on 13 Apr 2026 - 9:20

score 133 · Answer 12 · 2026-04-12 13:27:32

133

Views

why is the ratio $\frac{r^2}{t}$ important for solving the heat equation?

Published on 12 Apr 2026 - 13:27

score 166 · Answer 13 · 2026-04-09 08:10:43

166

Views

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score 323 · Answer 14 · 2026-04-23 12:59:21

323

Views

Solving Heat Equation with Transport Term

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score 172 · Answer 15 · 2026-05-10 12:34:39

172

Views

Find extension into higher dimensions for a matrix equation representing finite difference formulation of the heat equation

Published on 10 May 2026 - 12:34

List Question

Does accuracy of the numerical solution of a PDE depend on the scaling of the variables?

Heat Equation (Partial Differential Equation) - Fourier Transform Solution Form.

Laplace transform of heat equation in spherical coordinates

Show that $u^2$ satisfies $\partial_t(u^2) = 2k[\partial_x(u\partial_xu) - (\partial_x u)^2]$

Show that the norm $N_1(t) = \int_0^L(u(x,t) - u_0)^2dx$ is monotonically decreasing in time.

How to inverse a Fourier series?

Understanding Duhamel's principle, PDE

Solve heat equation with nonlinear term in matlab - Does my solution look reasonable?

Calculation/Verification of an integral kernel for $\operatorname{e}^{t\Delta}(1-\Delta)^{-\frac{1}{4}}$

Heat Equation with Antiperiodic BCs

1d PDE's on infinite Domains using fundamental solutions.

why is the ratio $\frac{r^2}{t}$ important for solving the heat equation?

Heat Equation with Inequality

Solving Heat Equation with Transport Term

Find extension into higher dimensions for a matrix equation representing finite difference formulation of the heat equation

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