We propose, analyze and test two novel fully discrete decoupled linearized algorithms for a nonlinearly coupled reaction-diffusion $N$-species competition model with harvesting or stocking effort. The time-stepping algorithms are first and second order accurate in time and optimally accurate in space. Stability and optimal convergence theorems of the decoupled schemes are proven rigorously. We verify the predicted convergence rates of our analysis and efficacy of the algorithms using numerical experiments and synthetic data for analytical test problems. We also study the effect of harvesting or stocking and diffusion parameters on the evolution of species population density numerically, and observe the co-existence scenario subject to optimal harvesting or stocking.
翻译:我们提议、分析和测试两个全新的完全分离的、完全分离的线性化算法,用于非线性结合的反应扩散(N$$-物种)的竞争模式,进行收获或储存努力。时间步骤算法在时间和空间上都是第一和第二顺序的准确和最佳精确。脱钩计划的稳定性和最佳趋同理论被证明是严格的。我们用数字实验和合成数据来核实我们分析算法的预测趋同率和效力,以便分析测试问题。我们还研究采伐或储存和传播参数对物种数量密度演变的影响,并观察以最佳收获或储存为条件的共存情景。