This book explains a step by step approach taken to develop a hybrid finite difference scheme from finite difference and operator splitting for the 2-D linear parabolic equation. Among the hybrid schemes developed are the Crank-Nicholson -Du Fort and Frankel, Crank-Nicholson-Lax-Friedrichs' and Crank-Nicholson- Du Fort and Frankel-Lax-Friedrichs' method. Crank-Nicholson-Du-Fort and Frankel is a hybrid scheme made by blending the Crank-Nicholson with Du-Fort and Frankel schemes. The Crank-Nicholson-Lax-Friedrichs' scheme is a hybrid scheme made by blending the Crank-Nicholson with Lax-Friedrichs' scheme. Crank-Nicholson-Du-Fort and Frankel-Lax-Friedrichs' method is a hybrid scheme made by blending the Crank-Nicholson, Du-Fort and Frankel and Lax-Friedrichs' schemes. All the schemes developed are derived from the Crank-Nicholson method and so they are unconditionally stable. The findings are out of advanced research done and analysis was done by MATLAB. The book is highly recommended for researches and academicians with an interest in Numerical solutions of linear and non-linear equations.