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The aim of this paper is to design some accurate artificial boundary conditions for the semi-discretized linear Schrödinger and heat equations in rectangular domains. The Laplace transform in time and discrete Fourier transform in space are applied to get Green’s functions of the semi-discretized equations in unbounded domains with single-source. An algorithm is given to compute these Green’s functions accurately through some recurrence relations. Furthermore, the finite-difference method is used to discretize the reduced problem with accurate boundary conditions. Numerical simulations are presented to illustrate the accuracy of our method in the case of the linear Schrödinger and heat equations. It is shown that the reflection at the corners is correctly eliminated. [ABSTRACT FROM AUTHOR]

The Asian monsoon affects the natural patterns of climate in China and its origin and evolution have been a matter of much debate in palaeoclimatology. Results from recent studies indicate that the Asian monsoon had reached the subtropical zone by at least c. 41 Ma and expanded to the central Tibetan Plateau during the Late Oligocene, although more geological evidence is required to confirm its spatial and temporal evolution. The well-developed Late Oligocene palaeosol in the Lunpola Basin, central Tibetan Plateau is an ideal material for addressing the issue. Observations of various climatic indicators suggest that these palaeosols were forest cinnamon soils, as shown by the compound Bt and Bk horizons, abundant clay coatings and carbonate nodules, and the diagnostic chemical composition of clays in the Bt horizon. A high chemical weather index, the Rb/Sr ratios and high contents of illite/smectite mixed-layer minerals show that these palaeosols experienced intense weathering and leaching during pedogenesis. The mean annual temperature and mean annual precipitation during the developmental period of the palaeosols were 10.4–14.8°C and 615–1128 mm, respectively, as estimated by empirical formulas, which are comparable with those of cinnamon soils in current monsoon climates. This study provides important independent evidence from palaeosols for studies of the evolution of the Asian monsoon. Supplementary material: The data about the clay chemical composition and climatic indicators of palaeosol and modern soils are available at https://doi.org/10.6084/m9.figshare.c.6850703 Thematic collection: This article is part of the Mesozoic and Cenozoic tectonics, landscape and climate change collection available at: https://www.lyellcollection.org/topic/collections/mesozoic-and-cenozoic-tectonics-landscape-and-climate-change [ABSTRACT FROM AUTHOR]