## Galerkins method for solving 2nd-order homogeneous, constant coefficients BVP

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Implement Galerkin method over the entire domain for solving 2nd order BVPs

Updated 10 Jan 2013

The purpose of this program is to implement Galerkin method over the entire domain 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_Galerkin1(a,b,c,t1,t2,x1,x2,n)
where "n" is the number of trial functions.
The output of this program is
1- The approximated solution of x(t) vs. exact solution of x(t)
2- The approximated x'(t) vs. exact x'(t)
3- The approximated x"(t) vs. exact x"(t)
Example:
x"(t)+ x'(t)+ x(t)=0
Boundary values:
x(1)=2, x(10)=0;
Solution: We have: a=1; b=1; c=1;
t1=1; t2=10;
x1=2; x2=0;
Using n=8 trial functions,
>>BVP_Galerkin(1,2,3,1,10,2,0,8)

### Cite As

Dr. Redmond Ramin Shamshiri (2021). Galerkins method for solving 2nd-order homogeneous, constant coefficients BVP (https://www.mathworks.com/matlabcentral/fileexchange/39794-galerkins-method-for-solving-2nd-order-homogeneous-constant-coefficients-bvp), MATLAB Central File Exchange. Retrieved .

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