Explicit and Implicit Methods In Solving Differential Equations

Differential equations are equations that involve an unknown function and derivatives. Euler's method are efficient methods to yield fairly accurate approximations of the actual solutions. By manipulating such methods, one can find ways to provide good approximations compared to the exact solution of parabolic partial differential equations and nonlinear parabolic differential equations.

Bentgrass response to K fertilization and K release rates from eight sand rootzone sources used in putting green construction.

There is a lack of plant response to fertilizer K in some sandy soils even though routine soil tests for soil available K are shown to be low. This lack of plant response to K fertilizer application may be explained by K release from nonexchangeable forms. Greenhouse and laboratory experiments were conducted to evaluate (a) response of bentgrass (Agrostis palustris [Agrostis stolonifera var. palustris]) cv. Pencross grown in rootzones with different sand sources to K fertilizer application and (b) K release from nonexchangeable forms from the different sand sources as an index to K availability. Experimental variables in the greenhouse were 2 K levels (0 and 250 mg K/kg soil) and 8 sand rootzone sources. Rootzone soils were sub-irrigated to ensure no K loss from leaching. Two laboratory methods (boiling 1 M HNO3 extraction and continuous leaching with 0.01 M HCl) and total K uptake by the bentgrass were employed to index K release from nonexchangeable forms for each rootzone source. K fertilizer application significantly increased bentgrass yield growing in one rootzone source and root weight in 3 rootzone sources. K uptake by bentgrass and the 2 laboratory methods showed important differences in K release from the sand rootzones. The K removed by the 2 laboratory methods was closely related to leaf tissue K and K uptake, with the 1 M HNO3 extraction method providing the closest fit. The release of K from primary minerals in some rootzones with high sand content is proceeding at rates to satisfy bentgrass requirements for K. The 1 M HNO3 extraction method may provide an alternative to the routine laboratory procedures presently being used to measure the extractable K in sand-based constructed putting greens by measuring K contributed by nonexchangeable forms.