Analytical solutions of some special nonlinear partial differential equations using Elzaki-Adomian decomposition method

We apply the Elzaki-Adomian Decomposition Method (EADM) in this study to solve nonlinear Benjamin-Bona-Mahony (BBM) and Fisher's partial differential equations (PDE). This method, being an integral transform, is a hybrid of two well-known and efficient methods: the Elzaki transform and the Adomian decomposition method. The method is demonstrated by solving two special cases of the BBM Equation and one special case of Fisher's partial differential equation. Because of its high convergence rate in approximating exact solutions, this approach is very dependable. The method can also produce numerical solutions without the usage of restrictive assumptions or the discretization typical of numerical methods; making it free of round-off errors. The Elzaki-Adomian Decomposition method employs a straightforward computation that leads to effectiveness. The efficiency of EADM is demonstrated in the significant reduction of number of numerical computations. The effectiveness and efficiency of EADM account for its broad application, particularly for higher order PDEs

Integrated use of fertilizer micro-dosing and Acacia tumida mulching increases millet yield and water use efficiency in Sahelian semi-arid environment

Limited availability of soil organic amendments and unpredictable rainfall, decrease crop yields drastically in the Sahel. There is, therefore, a need to develop an improved technology for conserving soil moisture and enhancing crop yields in the Sahelian semi-arid environment. A 2-year field experiment was conducted to investigate the mulching effects of Acacia tumida pruning relative to commonly applied organic materials in Niger on millet growth, yields and water use efficiency (WUE) under fertilizer micro-dosing technology. We hypothesized that (1) A. tumida pruning is a suitable mulching alternative for crop residues in the biomass-scarce areas of Niger and (2) combined application of A. tumida mulch and fertilizer micro-dosing increases millet yield and water use efficiency. Two fertilizer micro-dosing options (20 kg DAP ha−1, 60 kg NPK ha−1) and three types of organic mulches (millet straw, A. tumida mulch, and manure) and the relevant control treatments were arranged in factorial experiment organized in a randomized complete block design with four replications. Fertilizer micro-dosing increased millet grain yield on average by 28 %. This millet grain yield increased further by 37 % with combined application of fertilizer micro-dosing and organic mulch. Grain yield increases relative to the un-mulched control were 51 % for manure, 46 % for A. tumida mulch and 36 % for millet mulch. Leaf area index and root length density were also greater under mulched plots. Fertilizer micro-dosing increased WUE of millet on average by 24 %, while the addition of A. tumida pruning, manure and millet increased WUE on average 55, 49 and 25 %, respectively. We conclude that combined application of micro-dosing and organic mulch is an effective fertilization strategy to enhance millet yield and water use efficiency in low-input cropping systems and that A. tumida pruning could serve as an appropriate mulching alternative for further increasing crop yields and water use efficiency in the biomass-scarce and drought prone environment such as the Sahel. However, the economic and social implications and the long-term agronomic effects of this agroforestry tree in Sahelian millet based system have to be explored further

Derivation of Five-Stage Implicit Runge-Kutta Method of Order 10 via Gauss-Legendre Quadrature for Ordinary Differential Equations

This paper presents developing and implementing a five-stage implicit Runge-Kutta method of order ten via Gauss-Legendre quadrature for stiff or oscillatory first-order initial value problems (IVPs) of ordinary differential equations (ODEs). Using continuous collocation and interpolation techniques, the implicit Runge-Kutta method was developed by combining Legendre polynomials and exponential functions as the basis function. The properties of the method were investigated, and it was shown that it is consistent and A-stable. The new method was evaluated on two sampled problems involving stiffness and oscillation. The numerical results demonstrate that the new implicit Runge-Kutta is computationally efficient and outperforms previous methods of similar derivations.&nbsp