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

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

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Updated 04 Feb 2013

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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)

### Cite As

Dr. Redmond Ramin Shamshiri (2021). Galerkins method over "ne" elements for solving 2nd-order homogeneous, c.c BVP (https://www.mathworks.com/matlabcentral/fileexchange/40153-galerkins-method-over-ne-elements-for-solving-2nd-order-homogeneous-c-c-bvp), MATLAB Central File Exchange. Retrieved .

### Comments and Ratings (3)

Amitava Biswas

solmaz salehian

Zoltán Csáti

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!

##### MATLAB Release Compatibility
Created with R2010b
Compatible with any release
##### Platform Compatibility
Windows macOS Linux

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