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5.2 Exercises 183 such situations because the solution changesmore andmore slowly, but the time stepmust still bekept small, and it takes“forever” toapproach the stationary state. This is yet another example why one needs implicit methods like the Backward Euler scheme. Exercise5.10: Solvea two-pointboundaryvalueproblem Solve the following two-pointboundary-valueproblem u00.x/D2; x2 .0;1/; u.0/D0; u.1/D1: Hint DoExercise5.9.Modifytheboundaryconditioninthecodesoit incorporates aknownvalue foru.1/. Filename:2ptBVP.py. OpenAccess This chapter is distributed under the termsof theCreativeCommonsAttribution- NonCommercial 4.0 International License (http://creativecommons.org/licenses/by-nc/4.0/), which permits any noncommercial use, duplication, adaptation, distribution and reproduction in anymediumor format, as long as you give appropriate credit to the original author(s) and the source, a link isprovided to theCreativeCommons licenseandanychangesmadeare indicated. The images or other third party material in this chapter are included in thework’s Creative Commons license, unless indicated otherwise in the credit line; if suchmaterial is not included in thework’s Creative Commons license and the respective action is not permitted by statutory regulation, users will need to obtain permission from the license holder to duplicate, adapt or reproduce thematerial.