Source Panel Method: System of Equations 

After solving for the geometric integral from the previous video (Iij), we have the expression for the normal velocity on a panel's control point in terms of variables we know. Since we have N unknowns (where N is the number of panels approximating the airfoil surface), we need N equations to solve the system.
This video goes through how to set up the system of equations that needs to be solved in order to obtain each panel's source strength.
===== RELEVANT VIDEOS =====
► Panel Methods Playlist
• How To: Run XFoil from...
► Panel Method Geometry
• Panel Method Geometry
► Building More Complex Flows
• Building More Complex ...
► Flow Around an Airfoil
• Flow Around an Airfoil...
► Normal Velocity Geometric Integral [I(ij)]
• Source Panel Method: N...
► Tangential Velocity Geometric Integral [J(ij)]
• Source Panel Method: T...
► Streamline Geometric Integral SPM [Mx(ij) and My(ij)]
• Streamline Geometric I...
===== NOTES =====
→ To solve the system of equations, I'm using the programmatic function (x = A\b). This takes care of the solution method for you, but you can also use your own Gaussian elimination solver, for instance. Here is a link to the MATLAB documentation for the solver:
www.mathworks....
===== ERRORS =====
→ If you see an error in the video, please let me know and I will include it here.
===== REFERENCES =====
Note: the links are Amazon affiliate links. If you do happen to want to buy the book and use the link below, it helps me out a little.
► Fundamentals of Aerodynamics, Anderson
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► Foundations of Aerodynamics, Kuethe and Chow
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► Theory of Wing Sections, Abbott and Doenhoff
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