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Interpolating and smoothing biquadratic spline 插值和平滑双二次样条
IF 0.7 4区 数学
Applications of Mathematics Pub Date : 1995-01-01 DOI: 10.21136/am.1995.134298
R. Kučera
{"title":"Interpolating and smoothing biquadratic spline","authors":"R. Kučera","doi":"10.21136/am.1995.134298","DOIUrl":"https://doi.org/10.21136/am.1995.134298","url":null,"abstract":"The paper deals with the biquadratic splines and their use for the interpolation in two variables on the rectangular mesh. The possibilities are shown how to interpolate function values, values of the partial derivative or values of the mixed derivative. Further, the so-called smoothing biquadratic splines are defined and the algorithms for their computation are described. All of these biquadratic splines are derived by means of the tensor product of the linear spaces of the quadratic splines and their bases are given by the so-called fundamental splines.","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"19 1","pages":"339-356"},"PeriodicalIF":0.7,"publicationDate":"1995-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77932588","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
An explicit modified method of characteristics for the one-dimensional nonstationary convection-diffusion problem with dominating convection 具有主导对流的一维非平稳对流扩散问题的显式特征修正方法
IF 0.7 4区 数学
Applications of Mathematics Pub Date : 1995-01-01 DOI: 10.21136/am.1995.134300
J. Dalík, H. Růžičková
{"title":"An explicit modified method of characteristics for the one-dimensional nonstationary convection-diffusion problem with dominating convection","authors":"J. Dalík, H. Růžičková","doi":"10.21136/am.1995.134300","DOIUrl":"https://doi.org/10.21136/am.1995.134300","url":null,"abstract":"We describe a numerical method for the equation $u_t + pu_x - varepsilon u_{xx} = f$ in $(0,1) times (0,T)$ with Dirichlet boundary and initial conditions which is a combination of the method of characteristics and the finite-difference method. We prove both an a priori local error-estimate of a high order and stability. Example 3.3 indicates that our approximate solutions are disturbed only by a minimal amount of the artificial diffusion.","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"183 1","pages":"367-380"},"PeriodicalIF":0.7,"publicationDate":"1995-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77484058","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Double points on characteristics 双点特征
IF 0.7 4区 数学
Applications of Mathematics Pub Date : 1995-01-01 DOI: 10.21136/am.1995.134301
O. Röschel
{"title":"Double points on characteristics","authors":"O. Röschel","doi":"10.21136/am.1995.134301","DOIUrl":"https://doi.org/10.21136/am.1995.134301","url":null,"abstract":"","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"1 1","pages":"381-390"},"PeriodicalIF":0.7,"publicationDate":"1995-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77519509","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Explicit two-step Runge-Kutta methods 显式两步龙格-库塔方法
IF 0.7 4区 数学
Applications of Mathematics Pub Date : 1995-01-01 DOI: 10.21136/am.1995.134306
Z. Jackiewicz, R. Renaut, M. Zennaro
{"title":"Explicit two-step Runge-Kutta methods","authors":"Z. Jackiewicz, R. Renaut, M. Zennaro","doi":"10.21136/am.1995.134306","DOIUrl":"https://doi.org/10.21136/am.1995.134306","url":null,"abstract":"The explicit two-step Runge-Kutta (TSRK) formulas for the numerical solution of ordinary differential equations are analyzed. The order conditions are derived and the construction of such methods based on some simplifying assumptions is described. Order barriers are also presented. It turns out that for order $ple 5$ the minimal number of stages for explicit TSRK method of order $p$ is equal to the minimal number of stages for explicit Runge-Kutta method of order $p-1$. Numerical results are presented which demonstrate that constant step size TSRK can be both effectively and efficiently used in an Euler equation solver. Furthermore, a comparison with a variable step size formulation shows that in these solvers the variable step size formulation offers no advantages compared to the constant step size implementation.","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"121 1","pages":"433-456"},"PeriodicalIF":0.7,"publicationDate":"1995-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74692542","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 30
Properly recorded estimate and confidence regions obtained by an approximate covariance operator in a special nonlinear model 在一个特殊的非线性模型中，用近似协方差算子得到正确记录的估计和置信区域
IF 0.7 4区 数学
Applications of Mathematics Pub Date : 1995-01-01 DOI: 10.21136/AM.1995.134305
G. Wimmer
{"title":"Properly recorded estimate and confidence regions obtained by an approximate covariance operator in a special nonlinear model","authors":"G. Wimmer","doi":"10.21136/AM.1995.134305","DOIUrl":"https://doi.org/10.21136/AM.1995.134305","url":null,"abstract":"","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"47 1","pages":"411-431"},"PeriodicalIF":0.7,"publicationDate":"1995-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82426804","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 12
Proceedings of the 2nd Summer Conference Numerical Modelling in Continuum Mechanics. Preface 连续介质力学数值模拟第二届夏季会议论文集。前言
IF 0.7 4区 数学
Applications of Mathematics Pub Date : 1995-01-01 DOI: 10.21136/am.1995.134288
M. Feistauer, R. Rannacher, K. Kozel
{"title":"Proceedings of the 2nd Summer Conference Numerical Modelling in Continuum Mechanics. Preface","authors":"M. Feistauer, R. Rannacher, K. Kozel","doi":"10.21136/am.1995.134288","DOIUrl":"https://doi.org/10.21136/am.1995.134288","url":null,"abstract":"","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"107 1","pages":"161-162"},"PeriodicalIF":0.7,"publicationDate":"1995-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77412627","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Fast multigrid solver 快速多网格求解器
IF 0.7 4区 数学
Applications of Mathematics Pub Date : 1995-01-01 DOI: 10.21136/am.1995.134274
P. Vanek
{"title":"Fast multigrid solver","authors":"P. Vanek","doi":"10.21136/am.1995.134274","DOIUrl":"https://doi.org/10.21136/am.1995.134274","url":null,"abstract":"In this paper a black-box solver based on combining the unknowns aggregation with smoothing is suggested. Convergence is improved by overcorrection. Numerical experiments demonstrate the efficiency.","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"112 1","pages":"1-20"},"PeriodicalIF":0.7,"publicationDate":"1995-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77920844","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 47
Functional equations and a theoretical model of DLTS 泛函方程与DLTS理论模型
IF 0.7 4区 数学
Applications of Mathematics Pub Date : 1995-01-01 DOI: 10.21136/am.1995.134308
V. Tryhuk
{"title":"Functional equations and a theoretical model of DLTS","authors":"V. Tryhuk","doi":"10.21136/am.1995.134308","DOIUrl":"https://doi.org/10.21136/am.1995.134308","url":null,"abstract":"The paper deals with a theoretical model of the Crowel-Alipanahi correlator. The model describes a new possible effect of the DLTS spectra-exponential and nonexponential transient capacitance, normal or anomalous spectra.","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"27 1","pages":"473-482"},"PeriodicalIF":0.7,"publicationDate":"1995-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87309377","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Coupling of chemical reaction with flow and molecular transport 化学反应与流动和分子运输的耦合
IF 0.7 4区 数学
Applications of Mathematics Pub Date : 1995-01-01 DOI: 10.21136/am.1995.134293
U. Maas
{"title":"Coupling of chemical reaction with flow and molecular transport","authors":"U. Maas","doi":"10.21136/am.1995.134293","DOIUrl":"https://doi.org/10.21136/am.1995.134293","url":null,"abstract":"During the last years the interest in the numerical simulation of reacting flows has grown considerably. Numerical methods are available, which allow to couple chemical kinetics with flow and molecular transport. However, the use of detailed physical and chemical models, involving more than 100 chemical species, and thus more than 100 species conservation equations, is restricted to very simple flow configurations like one-dimensional systems or two-dimensional systems with very simple geometries, and models are required, which simplify chemistry without sacrificing accuracy. In many chemically reacting flows chemical processes occur with time scales differing by many orders of magnitude (e.g., 10$^{-10}$ s to 1 s in combustion processes), whereas the time scales of flow, molecular transport, and turbulence usually cover a much smaller range of time scales. Based on local time scale analyses it is possible to decouple the fast (and thus not rate limiting) chemical processes. In this way the chemistry can be described in terms of a small number of governing reaction progress variables, and computations of complex reacting flow problems become possible. Examples for calculations with detailed and simplified chemistry are shown for various reacting flows, such as hypersonic reacting flows or combustion processes.","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"57 1","pages":"249-266"},"PeriodicalIF":0.7,"publicationDate":"1995-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75453041","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 27
Efficient numerical solution of mixed finite element discretizations by adaptive multilevel methods 混合有限元离散化的自适应多层方法的有效数值解
IF 0.7 4区 数学
Applications of Mathematics Pub Date : 1995-01-01 DOI: 10.21136/AM.1995.134292
R. Hoppe, B. Wohlmuth
{"title":"Efficient numerical solution of mixed finite element discretizations by adaptive multilevel methods","authors":"R. Hoppe, B. Wohlmuth","doi":"10.21136/AM.1995.134292","DOIUrl":"https://doi.org/10.21136/AM.1995.134292","url":null,"abstract":"We consider mixed finite element discretizations of second order elliptic boundary value problems. Emphasis is on the efficient iterative solution by multilevel techniques with respect to an adaptively generated hierarchy of nonuniform triangulations. In particular, we present two multilevel solvers, the first one relying on ideas from domain decomposition and the second one resulting from mixed hybridization. Local refinement of the underlying triangulations is done by efficient and reliable a posteriori error estimators which can be derived by a defect correction in higher order ansatz spaces or by taking advantage of superconvergence results. The performance of the algorithms is illustrated by several numerical examples.","PeriodicalId":55505,"journal":{"name":"Applications of Mathematics","volume":"115 1","pages":"227-248"},"PeriodicalIF":0.7,"publicationDate":"1995-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79042957","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 14
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