I know how to solve partial differential equations analytically and numerically (some methods) but I am unable to interpret the solutions.
For example I know how to use PDEtoolbox in MATLAB to draw PDE but when figure comes I am unable to interpret the figure.
Similarly I don't know how to say whether solution is stable or unstable or weak just by seeing the figure.
I am doing self study so I need a good book which covers all of these topics and also I am not good in real analysis so I can't handle a book which is based on it.
Please suggest me some good book regarding this.
Thank you
Try the following books,
$1.~~~$ "Elements of Partial Differential Equations" by Ian N. Sneddon
$2.~~~$ "Linear Partial Differential Equations for Scientists and Engineers" by Tyn Myint-U , Lokenath Debnath
$3.~~~$ "Partial Differential Equations with Fourier Series and Boundary Value Problems" by Nakhle H. Asmar
These will definitely help you to solve your problems.
Note: In this connection I would like to inform you that for real analysis try
"Introduction to Real Analysis" by Robert G. Bartle and Donald R. Sherbert
The book is extremely great and an absolute beginner can read and understand it with immense pleasure. No doubt it will help you to make you strong in this field.