Algorithms based on DQM with new sets of base functions for solving parabolic partial differential equations in (2+1)(2+1) dimension

This paper deals with the numerical computations of two space dimensional time dependent parabolic partial differential equations by adopting adopting an optimal five stage fourth-order strong stability preserving Runge Kutta (SSP-RK54) scheme for time discretization, and three methods of differential quadrature with different sets of modified B-splines as base functions, for space discretization: namely i) mECDQM: (DQM with modified extended cubic B-splines); ii) mExp-DQM: DQM with modified exponential cubic B-splines, and iii) MTB-DQM: DQM with modified trigonometric cubic B-splines. Specially, we implement these methods on convection-diffusion equation to convert them into a system of first order ordinary differential equations,in time which can be solved using any time integration method, while we prefer SSP-RK54 scheme. All the three methods are found stable for two space convection-diffusion equation by employing matrix stability analysis method. The accuracy and validity of the methods are confirmed by three test problems of two dimensional convection-diffusion equation, which shows that the proposed approximate solutions by any of the method are in good agreement with the exact solutions

Impact of Organic Farming on Yield and Quality of BASMATI Rice and Soil Properties

The management of soil organic matter is critical to maintain a productive organic farming system. No one source of nutrient usually suffices to maintain productivity and quality control in organic system. In addition, the inputs to supplement nutrient avail-ability are often not uniform presenting additional challenges in meeting the nutrient requirement of crops in organic systems. With this concept, a field experiment was conducted at the research farm of Indian Agricultural Research Institute, New Delhi, India during 2003-06 in rice-wheat-green gram cropping system. In this experiment, different treatments comprising organic amendments such as Blue Green Algae (BGA) 15kg/ha, Azolla 1.0 tonne/ha, Vermicompost and Farm Yard Manure (FYM) 5.0 tonne/ha each applied alone or in combination were tested in organic crop production. These treatments were compared with absolute control (N0P0K0) and recommended dose of chemical fertilizer (N80P40K40). In wheat crop Azotobacter replaced Azolla, but other treatments remained same. For rice, a scented variety ‘Pusa Basmati 1’ and for wheat and green gram HYVs were taken. Biomass of green gram was incorporated in soil after picking of pods and wheat was sown using zero tillage practice. The obser-vations on grain yield, contents of Fe, Zn, Mn and Cu in rice grains, insect pest inci-dence, soil nutrients and microbial activity were taken. Results revealed a significant enhancement in grain yield of rice over absolute control due to the application of different organic amendments applied alone or in combina-tions. Rice grain yield increased by 114 to 116.8% over absolute control when all the 4 organic amendments were applied altogether. The rice grain yield (4.0 t ha-1) obtained under combined application of four organic amendments was at par with the yield recorded under recommended dose of chemical fertilizer application. An interesting observation recorded was that there was no serious attack of any insect pest or dis-ease in organically grown crop. Soil microbial population (Actinomycetes, Bacteria, Fungi and BGA) enhanced due to the application of organic amendments in compari-son to absolute control as well as recommended fertilizer application that in turn re-sulted in a notable enhancement in soil dehydrogenase and phosphatase enzyme activity. Soil organic carbon and available phosphorus contents were also found to be significantly increased due to organic farming practice over control as well as chemical fertilizer application. Rice grain analysis for nutrients viz. Fe, Zn, Mn and Cu showed a significant increase in Fe and Mn content in the treatments having 2 or more organic amendments over control. Zn and Cu content also increased but the increment was significant with combined application of 3 or 4 organic amendments. The study revealed that addition of four organic amendments viz. BGA, Azolla, FYM and Vermicompost could give the optimum yield (4.05 t/ha) of organic Basmati rice and improve grain and soil quality