The implicit finite-difference formulae are derived from fractional expansion of derivatives which form tridiagonal matrix equations. ... This means that a high-order explicit method may be replaced by an implicit method of the same order resulting in a much improved performance.

What is difference between explicit and implicit finite difference methods?

Explicit methods calculate the state of a system at a later time from the state of the system at the current time, while implicit methods find a solution by solving an equation involving both the current state of the system and the later one.

What is meant by finite difference method?

The finite difference method (FDM) is an approximate method for solving partial differential equations. It has been used to solve a wide range of problems. These include linear and non-linear, time independent and dependent problems.