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 forresearches and academicians with an interest in Numerical solutions of linear and non-linear equations.