The sediment budget is a method to study the distribution of sediment in different parts of a river basin. This paper studies the sediment budget of the Yangtze River by analyzing the data on soil erosion, size distributions of sediment deposits, sediment load, and fluvial process. A method to determine the sediment budget for the Yangtze River is proposed in which the total soil erosion from the upstream reaches and tributaries is divided into two parts: sediment load transported to the Yichang station and sediment storage in the tributaries and gullies. Furthermore, the sediment load is divided into three parts: bed material load deposited in the middle and lower reaches for the fluvial process, wash load transported to the estuary, and sediment deposition in Tongting Lake. The sediment transported into the estuary is further divided into two parts: very fine sediment drifting to the ocean and sediment deposition in the estuary for land creation. There is a large sediment demand for (1) the fluvial process to reach the minimum stream power in the middle and lower reaches; (2) sediment mining for building material; and (3) land creation in the estuary. The riverbed profile in the middle and lower reaches is developing toward the equilibrium profile defined by the minimum stream power, but the impoundment of the Three Gorges Reservoir interrupts and modifies this fluvial process. The annual sediment load in the Yangtze River has reduced due to various human activities by about 100 × 106 t in the past 15 years. Thus there is a sediment shortage for land creation in the river mouth.

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In this paper, we present a class of new variants of Ostrowski's method with order of convergence seven. Per iteration the new methods require three evaluations of the function and one evaluation of its first derivative and therefore this class of methods has the efficiency index equal to 1.627. Numerical tests verifying the theory are given, and multistep iterations, based on the present methods, are developed.

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In this paper, we present some new modifications of Newton's method for solving non-linear equations. Analysis of convergence shows that these methods have order of convergence five. Numerical tests verifying the theory are given and based on these methods, a class of new multistep iterations is developed.