Naveed Ahmad2025-11-252025-11-252015https://escholar.umt.edu.pk/handle/123456789/12728In this thesis, two numerical methods, based upon Pade’s approximation to the matrix exponential function, for solving one dimensional heat diffusion equations with variable coefficients, are developed. These methods are L-stable and fifth order accurate in space and time. These methods are tested on heat conduction problems through a thermally insulated thin wire. The solution of these problems gives the temperature at any distance from one end of the wire after any time of the heat conduction. The methods are found to be highly accurate and stable.enThesis