【摘要】：近幾年來,具有年齡結(jié)構(gòu)種群系統(tǒng)被廣泛關(guān)注.然而,因此數(shù)值解的研究就顯得尤為重要.本文討論具有年齡結(jié)構(gòu)種群系統(tǒng)的數(shù)值解.該論文的研究內(nèi)容主要有以下幾個方面:(1)討論了具有年齡結(jié)構(gòu)種群擴散系統(tǒng)反問題的數(shù)值解.對原系統(tǒng)變形后建立了具有高精度的四階Pad(?)差分格式來計算種群的密度和擴散系數(shù),該格式的截斷誤差為O(Δt~2+h~4)并且無條件穩(wěn)定,所得結(jié)果能更準確的描述種群密度和擴散系數(shù).且數(shù)值算例驗證了方法的精確性和可靠性.(2)討論了具有年齡結(jié)構(gòu)隨機種群系統(tǒng)數(shù)值解問題.在線性增長條件下,利用Euler-Maruyama(EM)方法討論了數(shù)值解的階矩漸近有界性,并獲得了漸近有界性準則.通過數(shù)值算例對所得的結(jié)論進行了驗證.(3)將分裂倒向Euler法(SSBE)應用于具有年齡結(jié)構(gòu)隨機種群系統(tǒng),減弱了上一問題中的假設(shè)條件.首先討論了解的存在唯一性,其次利用離散半鞅收斂定理,建立了分裂倒向Euler法對應數(shù)值解的幾乎必然指數(shù)穩(wěn)定性的判定準則.最后,用數(shù)值算例驗證了所得的結(jié)果.
[Abstract]:In recent years, the population system with age structure has been widely concerned. However, the study of numerical solutions is particularly important. In this paper, the numerical solution of population system with age structure is discussed. The main contents of this paper are as follows: (1) numerical solution of inverse problem of population diffusion system with age structure is discussed. The fourth order Pad (?) with high accuracy was established after the original system was deformed. The difference scheme is used to calculate the population density and diffusion coefficient. The truncation error of the scheme is O (螖 t ~ 2 h ~ (4) and is unconditionally stable. The obtained results can more accurately describe the population density and diffusion coefficient. Numerical examples verify the accuracy and reliability of the method. (2) the numerical solution of stochastic population system with age structure is discussed. Under the condition of linear growth, the asymptotic boundedness of the moment of numerical solutions is discussed by using Euler-Maruyama (EM) method, and the asymptotic boundedness criterion is obtained. The results obtained are verified by numerical examples. (3) the split backward Euler method (SSBE) is applied to the stochastic population system with age structure, which weakens the hypothesis in the previous problem. First, the existence and uniqueness of the solution are discussed. Then, by using the convergence theorem of discrete semimartingale, the criterion of almost inevitable exponential stability of the corresponding numerical solution of the split backward Euler method is established. Finally, numerical examples are used to verify the results obtained.
【學位授予單位】：北方民族大學
【學位級別】：碩士
【學位授予年份】：2017
【分類號】：O241.8

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