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The purpose of this paper is to present an approach capable of solving Burgers' equation. Diagonal Padé approximation with a factorization scheme is applied to find numerical solutions of the one‐dimensional Burgers' equation by presenting explicit factoring the polynomials of the approximation. The numerical results obtained by this approach, for various values of viscosity, have been compared with the exact solution and are found to be in good agreement with each other.

In this paper, factorized diagonal Padé approach is applied to solve Burgers' equation. In this method, Burgers' equation is reduced to a system of ordinary differential equations and is solved piecewise analytically to obtain the solution of the problem.

The results of proposed approach show that when the obtained results are compared to similar methods, this approach gives better accuracy. Also, the graphs with small ν values satisfy the physical properties of the problem; therefore, the approach is promising for nonlinear problems.

The authors' experiments show that the applied method worked fine with Burgers' equation and they hope to extend it to some other nonlinear problems.

The proposed method is easy to implement and the given algorithm is easy to use, even for non experts. The approach is flexible to use high order Padé approximants.

In the approach described in the paper, Padé approximation is calculated in a different manner than the classical approach.

The main purpose of this study is to detect homogeneous housing market areas among 196 districts of 5 major cities of Turkey in terms of house sale price indices. The second purpose is to forecast these 196 house sale price indices.

In this paper, the authors use the monthly house sale price indices of 196 districts of 5 major cities of Turkey. The authors propose an autoregressive (AR) model-based fuzzy clustering approach to detect homogeneous housing market areas and to forecast house price indices.

The AR model-based fuzzy clustering approach detects three numbers of homogenous property market areas among 196 districts of 5 major cities of Turkey where house sale price moves together (or with similar house sales dynamic). This approach also provides better forecasting results compared to standard AR models by higher data efficiency and lower model validation and maintenance effort.

In this study, the authors could not use any district-based socioeconomic and consumption behavioral indicators and any discrete geographical and property characteristics because of the data limitation.

The finding of this study would help property investors for establishing more effective property management strategies by taking different geographical location conditions into account.

From the government side, knowing future rises, falls and turning points of property prices in different locations can allow the government to monitor the property price changes and control the speculation activities that cause a dramatic change in the market.

There is no previous research paper focusing on neighborhood-based clusters and forecasting house sale price indices in Turkey. At this point, it is the first academic study.