New Formulation of Time Weighted Residual Method for Solving Wave Propagation Problems in One and Two Dimensional Continuums Fatemeh Ahmadizadeh f.ahmadizadeh@cv.iut.ac.ir Date of Submission: September 19, 2020 Department of Civil Engineering Isfahan University of Technology, Isfahan 84156-83111, Iran Degree: M.Sc Language: Farsi Supervisors: Dr. Bijan Boroomand ( boromand@cc.iut.ac.ir ) Dr. Bashir Movahedian ( b.movahedian@cc.iut.ac.ir ) The purpose of this study is to provide new formulation for Time-Weighted Residual Method which would extended the scope of its application. Among the meshless methods that have been considered by researchers in recent years, there are methods which use exponential functions to solve problems, and TWRM is one of these methods. The restriction of these meshless methods is that they can only be used to solve differential equations with constant coefficients. The most significant merit of the new formulation is to eliminate this restriction; in addition, pre-integration is not indispensable in solving problems with this formulation, which simplifies the process of solving. In this thesis the process of obtaining new terms, the way of using them and effective factors on accuracy of the results in one-dimensional problems are explained initially. These terms are then expanded for two-dimensional problems. Then several examples are solved by this formulation. The problems are also solved by the Finite Element Method in order to verify the proposed method. The results obtained from solving various examples indicate the accuracy and speed of the method presented in this study compared to Finite Element Method. Keywords Time-Weighted Residual Method, Wave Propagation, One and Two Dimensional Continuums, Meshless Methods.