PDE |
BCs |
ICs |
Click for link to solution
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![{\displaystyle u_{xx}={\frac {1}{k}}u_{t}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/26e97ad415d9b1f32412750ce3fba5cb81da0a87) |
![{\displaystyle u(0,t)=0{\mbox{ }}u(L,t)=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/508bee0894c837d84ae7c1a408f6805d623874bd) |
![{\displaystyle u(x,0)=f(x)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ca093fdac61eb7caaac35db526d720decfa228c4) |
BVP_1D_heat_hom_dirichlet_hom
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![{\displaystyle u_{xx}={\frac {1}{k}}u_{t}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/26e97ad415d9b1f32412750ce3fba5cb81da0a87) |
![{\displaystyle u(0,t)=T_{1}{\mbox{ }}u(L,t)=T_{2}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8370f94e6d56c39a11f49582a80c12c19a577739) |
![{\displaystyle u(x,0)=f(x)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ca093fdac61eb7caaac35db526d720decfa228c4) |
BVP_1D_heat_hom_dirichlet_non_hom
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![{\displaystyle u_{xx}={\frac {1}{k}}u_{t}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/26e97ad415d9b1f32412750ce3fba5cb81da0a87) |
![{\displaystyle u_{x}(0,t)=0{\mbox{ }}u(L,t)=T_{1}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9276d8c0c926227006caafb4f091ca8d4c827a5e) |
![{\displaystyle u(x,0)=f(x)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ca093fdac61eb7caaac35db526d720decfa228c4) |
BVP_1D_heat_hom_neumann_dirichlet
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![{\displaystyle u_{xx}={\frac {1}{k}}u_{t}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/26e97ad415d9b1f32412750ce3fba5cb81da0a87) |
![{\displaystyle u_{x}(0,t)=-k(u(0,t)-A){\mbox{ }}u(L,t)=T_{2}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/e14b7933d2601502494c723ef24d2abe5ff7ea10) |
![{\displaystyle u(x,0)=f(x)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ca093fdac61eb7caaac35db526d720decfa228c4) |
BVP_1D_heat_hom_dirichlet_non_hom
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![{\displaystyle u_{xx}+g(x)={\frac {1}{k}}u_{t}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/617da1995136cdf460aea6334f861054fa09d427) |
![{\displaystyle u(0,t)=T_{1}{\mbox{ }}u(L,t)=T_{2}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8370f94e6d56c39a11f49582a80c12c19a577739) |
![{\displaystyle u(x,0)=f(x)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ca093fdac61eb7caaac35db526d720decfa228c4) |
BVP_1D_heat_hom_dirichlet_non_hom
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![{\displaystyle u_{xx}={\frac {1}{k}}u_{t}+k(u(x,t)-A)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2dc276efdf10dee2b548c111658efc72124458d4) |
![{\displaystyle u(0,t)=T_{1}{\mbox{ }}u(L,t)=T_{2}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8370f94e6d56c39a11f49582a80c12c19a577739) |
![{\displaystyle u(x,0)=f(x)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ca093fdac61eb7caaac35db526d720decfa228c4) |
BVP_1D_heat_nonhom_dirichlet_non_hom
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![{\displaystyle u_{xx}={\frac {1}{k}}u_{t}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/26e97ad415d9b1f32412750ce3fba5cb81da0a87) |
![{\displaystyle u(0,t)=T_{1}{\mbox{ }}u(L,t)=T_{2}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/8370f94e6d56c39a11f49582a80c12c19a577739) |
![{\displaystyle u(x,0)=f(x)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/ca093fdac61eb7caaac35db526d720decfa228c4) |
BVP_2D_Laplaces_hom_BCs_non_hom
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![{\displaystyle \displaystyle \nabla ^{2}u=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/beecbe26bc281e621762505e411f6502d02f5dbd) |
![{\displaystyle u_{y}(x,\pi )=x}](https://wikimedia.org/api/rest_v1/media/math/render/svg/25f3d6be07400e41d1cd895264af0daf004b6e53) |
none |
click here to see pdf of Maple file that has solution.
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![{\displaystyle \displaystyle u_{xx}=u_{tt}+10}](https://wikimedia.org/api/rest_v1/media/math/render/svg/91e35b3167ed006f015fbe75cbccd5ff3cd2c93f) |
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![{\displaystyle u_{t}(x,0)=x(1-x)}](https://wikimedia.org/api/rest_v1/media/math/render/svg/72884e0f15f71fa6187464a6fdd05cbd0d9ed125) |
Click here to see pdf of a Maple file that has solution.
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![{\displaystyle \displaystyle \nabla ^{2}u={\frac {1}{4}}u_{t}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/a5b052b23a66e98452dbf3c76a6dd4d309a29be3) |
![{\displaystyle u(3,y,t)=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/7a779bbd075c6356e38d89255a260d51af41d2e8) |
![{\displaystyle u(x,y,t)=sin({\frac {\pi x}{3}})sin({\frac {\pi y}{5}})}](https://wikimedia.org/api/rest_v1/media/math/render/svg/9cf331423f69b49bc3b3b2562ce9e5e99111e385) |
click here to see pdf of Maple file that has solution.
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+ F(x,y,t) |
![{\displaystyle u(L,y,t)=0}](https://wikimedia.org/api/rest_v1/media/math/render/svg/cc740c45477906f4323731858549e6c36b8b273e) |
![{\displaystyle u(x,y,t)=sin({\frac {\pi x}{L}})sin({\frac {\pi y}{M}})}](https://wikimedia.org/api/rest_v1/media/math/render/svg/2a643e2fc7b7d631e3a8e26189ca04b287353070) |
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