Many software systems have been produced under host-concentrated development environment. However, at present, the software development environment has been changing into distributed development environment because of the progress of network computing technologies. Many software reliability growth models (SRGM's) based on nonhomogeneous Poisson processes are discrete state space models, and these models have not treated the software fault-detection process as a stochastic process with a continuous state space. In this paper, we propose an SRGM based on a stochastic process with a continuous state space for distributed development environment by applying a mathematical technique of stochastic differential equations.
We present the Cosine-Chebyshev-Galerkin method for solving the Poisson equation on a fan-shaped domain. The key to the efficiency of our method is to map the domain to a semi-infinite domain by using a new type of the double exponential formula. Not only the discrete system but also approximate solutions can be obtained rapidly by using the Fast Fourier Transform. Some numerical results show the efficiency of our proposed method.