In this paper, a novel Adomian decomposition method (ADM) is developed for the solution of Burgers' equation. While high level of this method for differential equations are found in the literature, this work covers most of the necessary details required to apply ADM for partial differential equations. The present ADM has the capability to produce three different types of solutions, namely, explicit exact solution, analytic solution, and semi‐analytic solution. In the best cases, when a closed‐form solution exists, ADM is able to capture this exact solution, while most of the numerical methods can only provide an approximation solution. The proposed ADM is validated using different test cases dealing with inviscid and viscous Burgers' equations. Satisfactory results are obtained for all test cases, and, particularly, results reported in this paper agree well with those reported by other researchers.

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A built environment with high-quality esthetic expression can positively contribute to key agendas of urban development. Environmental design is the design of physical environments that mainly respond to people’s behavioral needs and sensory preferences based on environment–behavior relations. Practitioners in this industry often work on esthetic quality improvement. Although previous studies have provided valuable knowledge about important elements of built environment esthetic expression, limited research efforts have been devoted to building a systematic framework that comprises key evaluation elements with high local adaptability and the influence relationships among them. The standards and preferences of esthetic expression in environmental design scheme evaluation are context-based. Providing an effective way to clarify evaluation elements with high local adaptability and the relationships among them may help reduce ambiguity, enhance consensus, and increase efficiency in the decision-making process. Therefore, this study adopted the esthetic expression evaluation of environmental design in China as an example and produced a hybrid decision analysis model by integrating the fuzzy Delphi method (FDM), exploratory factor analysis (EFA), analytic hierarchy process (AHP), and decision-making trial and evaluation laboratory (DEMATEL) method to evaluate the esthetic expression of environmental design schemes. A hierarchical evaluation framework composed of 5 dimensions and 18 evaluation elements was constructed in this study. The key design elements under each dimension and the influence relationships among them were also identified. This paper offers insights into the theoretical investigation and practical development of a systematic evaluation of the esthetic expression of environmental design schemes.