Proceedings of 1 st Ahmad Dahlan International Conference on Mathematics and Mathematics Education Universitas Ahmad Dahlan, Yogyakarta, 13-14 October 2017 94 A Dual Reciprocity Boundary Element Method for Water Infiltration Problems in a Single Flat and Trapezoidal Irrigation Channels Munadi, Imam Solekhudin, Sumardi, Atok Zulijanto Department of Mathematics, Faculty of Mathematics and Natural Sciences, Gadjah Mada University, Yogyakarta 55281, Indonesia E-mail : munadi76@gmail.com Abstract. Governing equation of the problem involving infiltration in homogeneous soils is Richard's Equation. This equation can be studied more conveniently by transforming the equation to a modified Helmholtz equation. In this study, a dual-reciprocity boundary element method (DRBEM) is employed to solve the modified Helmholtz equation numerically. Using the solutions obtained, numerical values of the matric flux potensial are then computed. The proposed method is tested on problems involving infiltration from a single flat and trapezoidal irrigation channels in a homogeneous soil. The numerical solutions of both channels are then compared. 1. Introduction Studies of infiltration problems in homogeneous soils have been considered by numerous researchers, for instance Azis et al. [3], Batu [2], Clements et al. [4], Lobo et al. [6], and Solekhudin [8]. These problems were solved analytically only for very simple cases, such as those considered by Batu. For more realistic, and hence more complicated cases, numerical methods may be needed. Moreover, although analytical methods may be regarded as successful to a certain extent, it is still useful to develop alternative numerical approaches. One approach worth considering is the dual- reciprocity boundary element method (DRBEM), which is known for its flexibility and accuracy in dealing with boundary conditions in many problems. In this paper, we study problem involving time independent water flow in unsaturated soils from a trapezoidal channel. To solve the problem, the governing equation, a Richards equation, is transformed into a modified Helmholtz equation. To do so, a set of transformations is employed. The modified Helmholtz equation is then solved numerically using a DRBEM. An example of infiltration from single trapezoidal channel is considered to test the method. The solutions obtained are then compared to those obtained from single flat channel. 2. Problem Formulation In the study of steady infiltration problems, the governing equation that is often used is   (()   )+   (()   )= ()  (1)