高階方程式 的英文怎麼說

中文拼音 [gāojiēfāngchéngshì]
高階方程式 英文
equation of higher order
  • 高 : Ⅰ形容詞1 （從下向上距離大; 離地面遠） tall; high 2 （在一般標準或平均程度之上; 等級在上的） above...
  • 階 : 名詞1. （臺階） steps; stairs 2. （等級） rank 3. [醫學] （耳蝸的三個螺旋管的任一個） scala 4. [數學] order 5. [地質學] stage
  • 方 : Ⅰ名詞1 （方形; 方體） square 2 [數學] （乘方） involution; power 3 （方向） direction 4 （方面） ...
  • 程 : 名詞1 （規章; 法式） rule; regulation 2 （進度; 程序） order; procedure 3 （路途; 一段路） journe...
  • 式 : 名詞1 （樣式） type; style 2 （格式） pattern; form 3 （儀式; 典禮） ceremony; ritual 4 （自然科...
  • 高階 : high [higher] order高階導數 higher derivative; higher order derivative; derivative of higher orde...
  • 方程式 : capeta
  1. By making some assumptions, collision frequency were presented. then the the flocculation kinetics model was established through population balance equation. comparison of experimental data and modeling results indicate that there are the same trend between the two. so the model can predict floes number and size during flocculation of yellow river ' s loess particles without using empirical parameters. the tem and sem were used to obsever floes in the study of floe structure. the flocculation was divided as flocculi, floc and floe aggregate. the floes structure model was established by assumption that particles position in floe accords with tetrahedron. the fractal dimension of model and experimental floes was found to be coincidentso the model can reflect the structure of flocs formed in flocculation of yellow river ' s loess particles by macromolecule flocculant at a certain extent

    最後，本文還對絮凝動力學和絮體結構進行了研究，在前人研究的基礎上，針對高分子絮凝黃河泥沙，對絮凝過程作了一些符合試驗條件的假設，建立了顆粒碰撞頻率表達式，應用了顆粒數量平衡方程，從而建立了絮凝過程的動力學生長模型，模型計算結果與試驗數據對比表明，二者趨勢一致，在沒有使用經驗參數的情況下基本上能夠描述黃河泥沙絮凝過程中絮體數量和尺寸分佈的變化過程；對絮體結構的研究中，應用掃描電子顯微鏡和透射電子顯微鏡對絮體進行了觀察，將絮體分為絮粒、絮團和絮網三個不同的生長階段，通過假設顆粒結合位置符西安建築科技大學博士學位論文合正四面體，建立了絮體結構模型，計算得到的模型絮體分形維數基本與試驗中的實際絮體相符，在一定程度上能夠反映高分子絮凝黃河泥沙生成的絮體結構。
  2. A composite 4 - th order adams - bashforth - moulton scheme is used to solve the equations. with this higher - order scheme, the accuracy of numerical computation results is well ensured

    採用四階精度的abm預測-校正差分格式，基本滿足了高階boussinesq方程對數值格式的要求。
  3. The most achievement is that we firstly obtain the analytic accurate solution of the modal fields of the waveguide structure and find some available character : ( 1 ) the different uniaxial crystal materials have the different propagation properties ; ( 2 ) when the optical axis of the crystal is on the plane that is made up of the normal direction of the waveguide plane and the propagation, there are te mode and tm mode in this special waveguide, but the principal mode is different of the character of the uniaxial crystal, the principal mode is the principal mode of te mode for the negative uniaxial crystal, but the one of tm mode for the positive uniaxial crystal ; ( 3 ) when the crystal optical - axis parallel to the waveguide plane, for the positive uniaxial crystal material, the principal mode of the waveguide is a te wave, which can be excited by the light at any frequency ; when the light frequency satisfies a single mode propagation condition, there will be only the principal mode propagating in the waveguide, otherwise some of the higher order modes can be excited, which are neither te modes, nor tm modes, but the hybrid guided modes

    本文就是在此背景下，利用金屬波導和單軸晶體的一些特性，結合麥克斯韋方程組和波導的邊界條件，從三種不同的情況研究了光在對稱平面單軸晶體金屬波導（波導層是單軸晶體，兩個波導界面均為金屬）內的傳輸特性，其主要貢獻為，首次解析地得到了這種波導結構下模式場的精確解，並發現了一些有用的特性： （ 1 ）模式場的性質因單軸晶體的性質不同而異； （ 2 ）當單軸晶體光軸位於波導界面法方向與傳輸方向構成的平面內時，波導中傳輸te波和tm波，只不過其主模因單軸晶體的性質不同而異，當波導層介質為負單軸晶體時，波導主模是te波主模，而波導層介質為正單軸晶體時波導主模是tm波主模。 （ 3 ）當單軸晶體光軸位於波導面內時，對于正單軸晶體，波導的主模是橫電波te _ 0模，任何頻率的光波均可激勵該模式；當光波波長滿足一定條件時，波導內傳輸單模，否則，將激勵起高階模式，高階模即匪te波，也匪tm波，而是兩者耦合而成的混合模。
  4. In this paper, high - order accurate weighted essentially non - oscillatory ( weno ) schemes are investigated and their applications in hyperbolic conservation laws are discussed. based on this, a new weno difference scheme which based on dispersion - relation - preserving relation is developed, and representative test cases with this scheme for computational aeroacoustics ( caa ) problems has been implemented and compared in order to test capability of wave capturing ; in addition, weno schemes generally do not converge at high order in the presence of contact discontinuity of euler equations, so a conservative front tracking technique coupling weno schemes and level set method to simulate the translating density profile is presented here, and numerical simulation with this technique for representative test case has been implemented and results show the desired accuracy

    本文研究了高階精度加權基本無振蕩（ weno ）格式及其在雙曲守恆律方程中的應用，在此基礎上作了兩個方面的工作：一是針對高頻聲波問題構造出一種基於保色散關系（ drp ）的weno有限差分格式，並對計算氣動聲學（ caa ）問題的代表性算例進行了大量數值實驗，比較了該格式捕捉波數的能力；另外，針對高階weno格式在處理euler方程的接觸間斷時精度有所降低的問題，研究了利用界面追蹤技術levelset方法和高階激波捕捉weno格式相結合的一種守恆追蹤方法，並且給出有代表性的密度滑移面問題的算例，得到一致高階精度的數值模擬結果。
  5. A normal transform is introduced, and there are enough much grids in the region between the critical layer and the wall, where the variation of the disturbance is the quickest. the finite - difference of governing equations with fourth - order accuracy in the normal direction is utilized in full regions including points close the wall, and is very important for accurately discreting equations. the combination of global and local methods is implemented, and a new iterative formula is derived

    對于曲線坐標系下的拋物化穩定性方程，文中發展了求解的高效數值方法:引進法向變換，使得在臨界層與壁面之間的擾動量變化最快的區域有更多的法向網格點;導出包含邊界鄰域在內的完全四階精度的法向有限差分格式，這對方程精確離散至關重要;採用全局法和局部法相結合的方法及其新的迭代公式，大大加速收斂並得到更精確的特徵值。
  6. In this paper, we develop the high - order accurate essentially non - oscillatory ( eno ) schemes on one and two - dimensional structured meshes in the finite volume formulation, and discuss their applications in hyperbolic conservation laws

    本文構造了一維、二維結構網格中的高階精度基本無振蕩（ eno ）有限體積格式，並且討論了它在雙曲守恆型方程中的應用。
  7. Considering enough the property of the equa - tion, we prove existence of absorbing set of the solution in h ~ ( 1 ) by the method of changeing the higher order nonlinear term as nonnegative guadratic form and prove existence of absorbing set of the solution in h ~ ( 2 ) by the method of linear combining of energy inequality and multiform classical inequality

    我們充分考慮方程的特點，將高階非線性項化為一非負定二次型使得解在h ~ 1中的吸收集的存在性得以證明。通過能量估計的巧妙組合以及多種形式的不等式進行精細的估計以獲得h 「的吸收集的存在性
  8. The increase - order of solutions of higher order homogeneous linear differential equations with polynomial coefficients

    多項式系數高階齊次線性微分方程解的增長級
  9. In this paper, we investigate the increase - order of solutions of higher order homogeneous linear differential equations with polynomial coefficients. we have obtained the precise result

    摘要研究了多項式系數高階齊次線性微分方程解的增長級問題，得到了比前人更精確的結果。
  10. A two - layer implicit difference schemes for solving parabolic equation of higher oder

    高階拋物型方程的兩層隱式差分格式
  11. A family of implicit difference schemes for solving the parabolic equation of higher order

    解高階拋物型方程的一族隱式差分格式
  12. A two layer implicit difference schemes of high accuracy for solving four order parabolic equations

    四階拋物型方程一個兩層的高精度隱式格式
  13. A class of three - layer implicit difference schemes of high accuracy for solving four order parabolic equations

    四階拋物型方程一族三層的高精度隱式格式
  14. Based on the previous work, the equations of motion and elastodynamics are changed. a high - order staggered velocity - stress finite - difference formula of the acoustic field in borehole are set up in cylindrical coordinate, and the corresponding code is accomplished

    本文在彈性波動力學的基礎上，將運動方程和本構方程作適當變形，採用交錯網格技術建立了井孔波動方程在柱坐標系下的速度?應力高階有限籌分公式，並編制了相關計算程序。
  15. The discretization process is deduced in detail, and the final iteration formula is given. in the discretization equations, higher order upwind differencing scheme is introduced into the calculation of the convection flux, whereas as for diffusion term, a central differencing scheme is taken into account

    文中就具體離散過程進行了推導，給出了最終的迭代公式，其中，對微分方程的離散採用顯式格式、對流項採用高階迎風差分格式、擴散項應用中心差分格式。
  16. In this paper, we expand eigenvalue of poisson equation using bilinear element, by the formulation of the error expanition, we can conclude that it is a upper bound. and by two numerical example, we computer the approximate eigenvalue of poisson equation in square and l - shape domains, then we analyses the approximate eigenvalue. we also extraplate the error expansion and enhance the accuracy of the eigenvalue form the second order to the forth order

    本論文對poisson方程的特徵值採用雙線性元進行展開，得到了誤差展開式，通過誤差展開式，我們能得到特徵值是上界。通過數值算例，計算方形與l形區域上的poisson方程的近似特徵值，並對數據進行分析，驗證了理論的正確性，然後通過對誤差展開式外推，收斂級數可以從二階提高到四階，得到了高精度的解。
  17. In this dissertation, the numerical computation for the acoustic radiation problem ( arp ) is studied deeply and systematically in the theory, method and the application technique, based on analyzing the situation of the home and abroad on the numerical computation for the acoustic radiation problem. the calculation formulas of the boundary element method ( bem ) for the exterior acoustic radiation problem in the full - space and half - space are deduced, based on the wave propagation theorem ; the arising of the non - unique solutions, which is associated with the application of the boundary integral equation ( bie ) in acoustic radiation problem, is analyzed and proofed ; the improved combined helmholtz integral equation formulation ( ichief ) is presented to overcome the non - uniqueness problem more effectively and reliably ; the determination of the singular integral coefficients on various occasions is analyzed ; the properties and treatments of the singular integrals with different orders axe studied ; the computation program of the cubic spline ichief is developed and its ability to overcome the non - uniqueness problem and feasibility to discrete the surface coarsely with the sufficient calculation precision are examined through examples

    第二章在聲波動理論基礎上，詳細地推導出對應于無限域和半無限域的外部振動聲輻射問題的邊界積分方程計算公式；根據fredholm積分理論，對利用邊界積分方程計算振動聲輻射問題過程中解的非唯一性的產生進行了分析和證明；改進了chief法以提高其克服解的非唯一性的有效性和可靠性；對不同條件下奇性系數的計算、強奇性積分的收斂性及其在變量替換時與普通積分的差異性、不同階奇性積分的計算、數值求積分等進行了研究；開發了三次樣條改進chief法計算軟體，並通過算例考核了該方法在特徵波數處克服解的非唯一性的有效性和在保證計算精度的前提下實現剖分粗化以提高計算效率的可行性。
  18. The momentum equations are integrated in time using the four - stage explicit jameson runge - kutta algorithm and discretized in space using fourth order accurate compact scheme as well as the pressure poisson equation

    動量方程的時間導數採用四步jamesonrunge - kutta法，空間導數和壓力poisson方程均採用四階高精度緊致格式。
  19. The solutions of the high step binomial coefficient type linear differential equation

    高階二項式系數型線性微分方程
  20. Different from the scattering theory used in the derivation of conventional generalized screen propagator, in this paper, a high order formula of generalized screen propagator for one - way wave equation is proposed by using the asymptotic expansion of single - square - root operator

    摘要不同於常規廣義屏傳播運算元的推導中使用散射理論，本文利用單平方根運算元的漸近展開，推導出了單程波方程廣義屏傳播運算元的高階表達式。
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