A parameter uniform method for two-parameter singularly perturbed boundary value problems with discontinuous data.

We consider two-parameter singularly perturbed problems of reaction-convection-diffusion type in one dimension. The convection coefficient and source term are discontinuous at a point in the domain. The problem is numerically solved using the upwind difference method on an appropriately defined Shishkin-Bakhvalov mesh. At the point of discontinuity, a three-point difference scheme is used. A convergence analysis is given and the method is shown to be first-order uniformly convergent with respect to the perturbation parameters. The numerical results presented in the paper confirm our theoretical results of first-order convergence. Summing up: • The Shishkin-Bakhvalov mesh is graded in the layer region and uniform in the outer region as shown in the graphical abstract. • The method presented here has uniform convergence of order one in the supremum norm. • The numerical orders of convergence obtained in numerical examples with Shishkin- Bakhvalov mesh are better than those for Shishkin mesh.

Occurrence of Arbuscular Mycorrhizal Fungi in Rhizosphere of Jatropha curcas L. in Arid and Semi Arid Regions of India.

A study was conducted to identify common arbuscular mycorrhizal (AM) fungi present in rhizosphere of Jatropha curcas L., an important bio-diesel crop, from different arid and semi arid regions of India viz., Jodhpur (Rajasthan), Hissar (Haryana), Jhansi and Lalitpur (Uttar Pradesh) and Hyderabad (Andhra Pradesh). A total of 20 AM species were recorded, which consisted of two species of Acaulospora and 18 species of Glomus. The highest frequency of occurrence was recorded for Glomus intraradix (100%), followed by Acaulospora scrobiculata (83%), G. etunicatum (50%) and Glomus 1 (50%). Maximum species richness was recorded at Jodhpur, followed by Jhansi, Hissar, Hyderabad and Lalitpur. The results seem to suggest that species richness was more in arid regions as compared to semi arid areas.

Effect of arbuscular mycorrhizal inoculations on seedling growth and biomass productivity of two bamboo species.

A study was conducted to identify suitable arbuscular mycorrhizal (AM) fungi for inoculation of Bambusa bambos and Dendrocalamus strictus at nursery stage for increasing growth and productivity. Twelve AM species, isolated from bamboo and other common trees of Bundelkhand were used for inoculations. In B. bambos, total dry weight and phosphorus (P) uptake were significantly increased by all studied fungi and shoot length was increased by eight AM inoculants. Maximum mycorrhizal dependency (MD) was recorded for Acaulospora scrobiculata (44.2%), followed by Glomus cerebriforme (41.6%) and G. intraradix (41.0%). In D. strictus, all tested AM inoculants significantly increased shoot length, dry shoot weight and P uptake, except Glomus 1. Dry root weight was significantly increased by only two inoculants namely, G. cerebriforme and G. etunicatum. Total dry weight was significantly increased by eight AM fungi. Maximum MD was recorded for G. cerebriforme (62.9%), followed by G. diaphanum (55.0%) and G. etunicatum (51.3%). Thus, the results showed that utilization of effective AM fungi can enhance the productivity of bamboo in the region.