ABSTRACT In present work, a one dimensional heat conduction problem with uniform heat generation is solved by using element free Gelerkin method (EFGM). The problem was to calculate the temperature distribution on different points across the thickness of a plane wall. The nodes are generated across the thickness of wall to find out the temperature distribution on different points. Then moving least squares (MLS) approximants is used to approximate the unknown function of temperature T(x) with the help of T h (x). Lagrange multiplier technique is used to enforce essential boundary conditions. The MATLAB codes have been developed to obtain the solution of the given problem. The results obtained by EFG method are compared with analytical and FEM results to validate the proposed MATLAB codes. The results are also studied by increasing the number of nodes and by changing the values of scaling parameter d max . Different weight functions are also used to check the variation in the results
