This means that we have N-2 equations, each of which involves an unknown U(i) and its.

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The forward time, centered space (FTCS), the backward time, centered space (BTCS), and Crank-Nicolson schemes are developed, and applied to a simple problem in1volving the one-dimensional heat equation.

Complete, working Matlab and FORTRAN codes for each program are presented.

The results of running the codes on finer (one-dimensional) meshes, and with smaller time steps are demonstrated.

The Matlab codes are straightforward and allow us to see the differences in implementation between explicit method (FTCS) and implicit methods (BTCS).

The codes also allow us to experiment with the stability limit of the FTCS scheme.

This report provides a practical overview of numerical solutions to the heat equation using the.

The finite difference method is one of several techniques for obtaining numerical solutions.

In.

In this context the word discrete means that the numerical solution is.

The mesh is the set of locations where the discrete solution is computed.

The core idea of the finite-difference method is to replace continuous derivatives with so called.

A simple, basic Fortran95 code is written to find the tangent of the function cos () by.

This approach uses the concept of discretization of space and.

Every equation is satisfied for each distinct point or steps and.

The above program illustrates the difference between the values obtained from actual derivatives and.

The difference between the two values gives the error due to the.

Figure 1. Differentiation of the function f(x) using (i) Finite Difference Method.

A FORTRAN95 program which applies the finite difference method to estimate the.

Since X(1) A and X(N) B, we can use the boundary conditions to.

If we rearrange the terms in this approximation, and set it equal to F(X(i)), we get the.

Heat Transfer In Metal Rod