Problem 316 ots Galerkin Method. Using the Galerkin Method, solve the following differential equation with an approximate solution of the form: ü(x) = c1$1+ C2$2 = C1x+ c2x². d?u +x² = 0 dx2 0

Problem 316 ots Galerkin Method. Using the Galerkin Method, solve the<br>following differential equation with an approximate solution of the form:<br>ü(x) = c1$1+ C2$2 = C1x+ c2x².<br>d?u<br>+x² = 0<br>dx2<br>0 <x<1<br>u(0) = 0<br>Boundary Conditions:} du<br>(1) = 1<br>dx<br>Compare your approximate solution with the exact one by plotting them on a<br>-1<br>4<br>graph. The exact solution is given by: u(x) =x* +;x. Also, compare the<br>4<br>12<br>3<br>derivatives du /dx and dũ/dx on a separate plot. What do you observe?<br>

Extracted text: Problem 316 ots Galerkin Method. Using the Galerkin Method, solve the following differential equation with an approximate solution of the form: ü(x) = c1$1+ C2$2 = C1x+ c2x². d?u +x² = 0 dx2 0 <><1 u(0)="0" boundary="" conditions:}="" du="" (1)="1" dx="" compare="" your="" approximate="" solution="" with="" the="" exact="" one="" by="" plotting="" them="" on="" a="" -1="" 4="" graph.="" the="" exact="" solution="" is="" given="" by:="" u(x)="x*" +;x.="" also,="" compare="" the="" 4="" 12="" 3="" derivatives="" du="" dx="" and="" dũ/dx="" on="" a="" separate="" plot.="" what="" do="" you="">

Jun 04, 2022

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Problem 316 ots Galerkin Method. Using the Galerkin Method, solve the following differential equation with an approximate solution of the form: ü(x) = c1$1+ C2$2 = C1x+ c2x². d?u +x² = 0 dx2 0

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