# Need to Compute Intermediate solutions of Heat equation

**URL:** <https://community.freefem.org/t/need-to-compute-intermediate-solutions-of-heat-equation/3720>\
**Category:** General Discussion\
**Created:** [January 31, 2025, 7:37pm UTC](https://community.freefem.org/t/need-to-compute-intermediate-solutions-of-heat-equation/3720 "2025-01-31T19:37:36Z")\
**Posts on this page:** 1\
**Page:** 1

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**Author:** ![Monirul25](https://yyz2.discourse-cdn.com/flex030/user_avatar/community.freefem.org/monirul25/32/3287_2.png) [@Monirul25](https://community.freefem.org/u/Monirul25)\
**Post date:** [January 31, 2025, 7:37pm UTC](https://community.freefem.org/t/need-to-compute-intermediate-solutions-of-heat-equation/3720/1 "2025-01-31T19:37:36Z")

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Hello, all experts, i have applied backward-Euler in Time dependent Heat equation. I am getting good results also. **I want to store the intermediate solutions** u^{1}, u^{2},…,u^{n-1}, where u^0 is the initial solution and u^{n} is the final solution. Then, i want to compute an expression:

> Blockquote  
> X=exp(-a\*(n-1)\*dt)_u\_{1}+exp(-a_(n-2)\*dt)_u\_{2}+…+exp(-a_dt)\*u\_{n-1}  
> Blockquote  
> , where n comes from space refinement loop and dt is time step (known), a=0.1(known). u^{1}, u^{2},…,u^{n-1} are all knowns intermediate solutions of Heat equations.  
> Here, is my Code.  
> [Heat.edp](https://community.freefem.org/uploads/short-url/rYsgT6cO2nsTNmsKmjOgmo9YaTK.edp) (2.2 KB)

Thanks in advance.