Finite difference method for boundary value problems involving transition conditions

We know that the classical finite difference method is intended for solving one-interval differential equations, and it is not clear how to apply this technique to two-interval differential equations that satisfy additional conditions of interaction between these two-intervals, the so-called transmission conditions. In this thesis we have adapted this method to two-interval differential equations satisfying not only boundary value conditions, but also additional transmission conditions. The modified Finite Difference Method was applied to some illustrative two-interval boundary-transmission problems. To demonstrate the applicability and efficiency of the proposed modification of Finite Difference method the obtained finite-difference solutions are compared graphically with the exact solutions, and the corresponding error analysis is also presented in tables. The obtained results show the applicability, efficiency and reliability of the proposed modified Finite Difference Method, developed in this thesis.