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### Highlights from Galerkins method over "ne" elements for solving 2nd-order homogeneous, c.c BVP

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# Galerkins method over "ne" elements for solving 2nd-order homogeneous, c.c BVP

### Dr. Ramin Shamshiri (view profile)

Implement Galerkin method over "ne" individual elements for solving 2nd order BVPs

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Description

The purpose of this program is to implement Galerkin method over "ne" individual elements for solving the following general 2nd order,
homogeneous, Boundary Value problem (BVP) with constant coefficients, and then comparing the answer with the exact solution.

ax"(t)+bx'(t)+cx(t)=0 for t1<=t<=t2
BC: x(t1)=x1 and x(t2)=x2

>> BVP_Galerkin(a,b,c,t1,t2,x1,x2,ne)
where "ne" is the number of elements

The output of this program is
1- The approximated x(t) vs. exact x(t)
2- The approximated x'(t) vs. exact x'(t)
3- The approximated x"(t) vs. exact x"(t)

Example:
x"(t)+ 0.5x'(t)+ 10x(t)=0
BC: x(1)=2, x(10)=0;
Solution: We have: a=1;b=2;c=3;
t1=1;t2=10;
x1=2;x2=0;
Using ne=128 elements,
>>BVP_Galerkin2(1,2,3,1,10,2,0,128)

MATLAB release MATLAB 7.11 (R2010b)
05 Feb 2013 solmaz salehian

### solmaz salehian (view profile)

04 Feb 2013 Zoltán Csáti

### Zoltán Csáti (view profile)

The code can be easily followed, however there are places where the program could be vectorized. Moreover the solution of the final linear system MUST NOT be solved with function inv!

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