In this dissertation exponential basis functions method (EBFs) has been developed for solving partial differential equations in 3D space and also for initial-boundary value equations. In this method the homogeneous part of differential equations is approximated in linear combination of exponential basis functions. A special transformation has been used for computing constant coefficients. Choosing fundamental basis which form solutions series plays an important role in exact computation of the equation solution. For this reason a new pattern has been proposed for choosing basis functions on the basis of determining the fluctuation measure of boundary conditions. The efficiency of this new pattern in solving some 2D equations has been investigated. Later on, after developing the formulation of EBFs method for solving 3D and initial-boundary value equations, the new pattern of choosing EBFs has been extended for solving these equations. EBFs method along with presenting new choosing pattern has been developed also for computing particular solution of 3D differential equations. Solving Laplace , Helmholtz and Elastic wave differential equations in EBFs method have been considered in this thesis as the most important and the most useful 3D equations. Also, as the first step in developing EBFs method solving two 1D transient heat equation and time dependent convection-diffusion have been investigated for solving initial-boundary value equations. The solved examples show that using EBFs method along with new choosing pattern is well enough able to solve different problems with any boundary conditions with fluctuations from low to high.