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Looking for a MATLAB expert to solve a two coupled PDE's through method of characteristics

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I am looking for an Expert who can can solve two coupled PDE's in MATLAB and provide the code. The problem needs to solved through method of characteristics method. A partially completed MATLAB code will be provided for further modification.  In the attached file, you may see the two coupled equations to be solved in a matrix form. Further details will be provided upon request. (initial and boundary conditions)

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