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A MESHLESS LOCAL GALERKIN INTEGRAL EQUATION METHOD FOR SOLVING A TYPE OF DARBOUX PROBLEMS BASED ON RADIAL BASIS FUNCTIONS 基于径向基函数的无网格局部伽辽金积分方程法求解一类达布问题
The ANZIAM journal Pub Date : 2021-10-01 DOI: 10.1017/S1446181121000377
P. Assari, F. Asadi-Mehregan, M. Dehghan
{"title":"A MESHLESS LOCAL GALERKIN INTEGRAL EQUATION METHOD FOR SOLVING A TYPE OF DARBOUX PROBLEMS BASED ON RADIAL BASIS FUNCTIONS","authors":"P. Assari, F. Asadi-Mehregan, M. Dehghan","doi":"10.1017/S1446181121000377","DOIUrl":"https://doi.org/10.1017/S1446181121000377","url":null,"abstract":"Abstract The main goal of this paper is to solve a class of Darboux problems by converting them into the two-dimensional nonlinear Volterra integral equation of the second kind. The scheme approximates the solution of these integral equations using the discrete Galerkin method together with local radial basis functions, which use a small set of data instead of all points in the solution domain. We also employ the Gauss–Legendre integration rule on the influence domains of shape functions to compute the local integrals appearing in the method. Since the scheme is constructed on a set of scattered points and does not require any background meshes, it is meshless. The error bound and the convergence rate of the presented method are provided. Some illustrative examples are included to show the validity and efficiency of the new technique. Furthermore, the results obtained demonstrate that this method uses much less computer memory than the method established using global radial basis functions.","PeriodicalId":74944,"journal":{"name":"The ANZIAM journal","volume":"15 1","pages":"469 - 492"},"PeriodicalIF":0.0,"publicationDate":"2021-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81988865","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
INDEX 指数
The ANZIAM journal Pub Date : 2021-10-01 DOI: 10.1017/s1446181121000213
{"title":"INDEX","authors":"","doi":"10.1017/s1446181121000213","DOIUrl":"https://doi.org/10.1017/s1446181121000213","url":null,"abstract":"","PeriodicalId":74944,"journal":{"name":"The ANZIAM journal","volume":"125 1","pages":"493 - 494"},"PeriodicalIF":0.0,"publicationDate":"2021-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77195928","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
BOUNDS ON THE CRITICAL TIMES FOR THE GENERAL FISHER–KPP EQUATION 一般fisher-kpp方程的临界时间的界
The ANZIAM journal Pub Date : 2021-10-01 DOI: 10.1017/S1446181121000365
M. Rodrigo
{"title":"BOUNDS ON THE CRITICAL TIMES FOR THE GENERAL FISHER–KPP EQUATION","authors":"M. Rodrigo","doi":"10.1017/S1446181121000365","DOIUrl":"https://doi.org/10.1017/S1446181121000365","url":null,"abstract":"Abstract The Fisher–Kolmogorov–Petrovsky–Piskunov (Fisher–KPP) equation is one of the prototypical reaction–diffusion equations and is encountered in many areas, primarily in population dynamics. An important consideration for the phenomena modelled by diffusion equations is the length of the diffusive process. In this paper, three definitions of the critical time are given, and bounds are obtained by a careful construction of the upper and lower solutions. The comparison functions satisfy the nonlinear, but linearizable, partial differential equations of Fisher–KPP type. Results of the numerical simulations are displayed. Extensions to some classes of reaction–diffusion systems and an application to a spatially heterogeneous harvesting model are also presented.","PeriodicalId":74944,"journal":{"name":"The ANZIAM journal","volume":"30 1","pages":"448 - 468"},"PeriodicalIF":0.0,"publicationDate":"2021-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76140119","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
IDEAL PLANAR FLUID FLOW OVER A SUBMERGED OBSTACLE: REVIEW AND EXTENSION 理想平面流体在水下障碍物上的流动:回顾与扩展
The ANZIAM journal Pub Date : 2021-10-01 DOI: 10.1017/S1446181121000341
L. Forbes, S. Walters, G. Hocking
{"title":"IDEAL PLANAR FLUID FLOW OVER A SUBMERGED OBSTACLE: REVIEW AND EXTENSION","authors":"L. Forbes, S. Walters, G. Hocking","doi":"10.1017/S1446181121000341","DOIUrl":"https://doi.org/10.1017/S1446181121000341","url":null,"abstract":"Abstract A classical problem in free-surface hydrodynamics concerns flow in a channel, when an obstacle is placed on the bottom. Steady-state flows exist and may adopt one of three possible configurations, depending on the fluid speed and the obstacle height; perhaps the best known has an apparently uniform flow upstream of the obstacle, followed by a semiinfinite train of downstream gravity waves. When time-dependent behaviour is taken into account, it is found that conditions upstream of the obstacle are more complicated, however, and can include a train of upstream-advancing solitons. This paper gives a critical overview of these concepts, and also presents a new semianalytical spectral method for the numerical description of unsteady behaviour.","PeriodicalId":74944,"journal":{"name":"The ANZIAM journal","volume":"68 1","pages":"377 - 419"},"PeriodicalIF":0.0,"publicationDate":"2021-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88483100","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
INTERACTION OF A SINGULAR SURFACE WITH A STRONG SHOCK IN THE INTERSTELLAR GAS CLOUDS 星际气体云中单一表面与强烈激波的相互作用
The ANZIAM journal Pub Date : 2021-07-01 DOI: 10.1017/S1446181121000328
J. Jena, S. Mittal
{"title":"INTERACTION OF A SINGULAR SURFACE WITH A STRONG SHOCK IN THE INTERSTELLAR GAS CLOUDS","authors":"J. Jena, S. Mittal","doi":"10.1017/S1446181121000328","DOIUrl":"https://doi.org/10.1017/S1446181121000328","url":null,"abstract":"Abstract We investigate the interaction between a singular surface and a strong shock in the self-gravitating interstellar gas clouds with the assumption of spherical symmetry. Using the method of the Lie group of transformations, a particular solution of the flow variables and the cooling–heating function for an infinitely strong shock is obtained. This paper explores an application of the singular surface theory in the evolution of an acceleration wave front propagating through an unperturbed medium. We discuss the formation of an acceleration, considering the cases of compression and expansion waves. The influence of the cooling–heating function on a shock formation is explained. The results of a collision between a strong shock and an acceleration wave are discussed using the Lax evolutionary conditions.","PeriodicalId":74944,"journal":{"name":"The ANZIAM journal","volume":"202 1","pages":"342 - 358"},"PeriodicalIF":0.0,"publicationDate":"2021-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73542047","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
ANZ VOLUME 63 ISSUE 3 COVER AND FRONT MATTER 澳新银行第63卷第3期封面和封面
The ANZIAM journal Pub Date : 2021-07-01 DOI: 10.1017/s1446181121000171
{"title":"ANZ VOLUME 63 ISSUE 3 COVER AND FRONT MATTER","authors":"","doi":"10.1017/s1446181121000171","DOIUrl":"https://doi.org/10.1017/s1446181121000171","url":null,"abstract":"","PeriodicalId":74944,"journal":{"name":"The ANZIAM journal","volume":"1 1","pages":"f1 - f2"},"PeriodicalIF":0.0,"publicationDate":"2021-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91228798","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
ANZ VOLUME 63 ISSUE 3 COVER AND BACK MATTER 澳新银行第63卷第3期封面和封底
The ANZIAM journal Pub Date : 2021-07-01 DOI: 10.1017/s1446181121000183
{"title":"ANZ VOLUME 63 ISSUE 3 COVER AND BACK MATTER","authors":"","doi":"10.1017/s1446181121000183","DOIUrl":"https://doi.org/10.1017/s1446181121000183","url":null,"abstract":"","PeriodicalId":74944,"journal":{"name":"The ANZIAM journal","volume":"27 1","pages":"b1 - b6"},"PeriodicalIF":0.0,"publicationDate":"2021-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91339538","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
OPTIMAL PORTFOLIO AND CONSUMPTION FOR A MARKOVIAN REGIME-SWITCHING JUMP-DIFFUSION PROCESS 马尔可夫状态切换跳跃扩散过程的最优投资组合和消费
The ANZIAM journal Pub Date : 2021-07-01 DOI: 10.1017/S1446181121000122
Caibin Zhang, Zhibin Liang, K. Yuen
{"title":"OPTIMAL PORTFOLIO AND CONSUMPTION FOR A MARKOVIAN REGIME-SWITCHING JUMP-DIFFUSION PROCESS","authors":"Caibin Zhang, Zhibin Liang, K. Yuen","doi":"10.1017/S1446181121000122","DOIUrl":"https://doi.org/10.1017/S1446181121000122","url":null,"abstract":"Abstract We consider the optimal portfolio and consumption problem for a jump-diffusion process with regime switching. Under the criterion of maximizing the expected discounted total utility of consumption, two methods, namely, the dynamic programming principle and the stochastic maximum principle, are used to obtain the optimal result for the general objective function, which is the solution to a system of partial differential equations. Furthermore, we investigate the power utility as a specific example and analyse the existence and uniqueness of the optimal solution. Under the constraints of no-short-selling and nonnegative consumption, closed-form expressions for the optimal strategy and the value function are derived. Besides, some comparisons between the optimal results for the jump-diffusion model and the pure diffusion model are carried out. Finally, we discuss our optimal results in some special cases.","PeriodicalId":74944,"journal":{"name":"The ANZIAM journal","volume":"3 1","pages":"308 - 332"},"PeriodicalIF":0.0,"publicationDate":"2021-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75248162","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
ALGORITHM TO CONSTRUCT INTEGRO SPLINES 构造整样条的算法
The ANZIAM journal Pub Date : 2021-07-01 DOI: 10.1017/S1446181121000316
Renchin-Ochir Mijiddorj, T. Zhanlav
{"title":"ALGORITHM TO CONSTRUCT INTEGRO SPLINES","authors":"Renchin-Ochir Mijiddorj, T. Zhanlav","doi":"10.1017/S1446181121000316","DOIUrl":"https://doi.org/10.1017/S1446181121000316","url":null,"abstract":"Abstract We study some properties of integro splines. Using these properties, we design an algorithm to construct splines \u0000$S_{m+1}(x)$\u0000 of neighbouring degrees to the given spline \u0000$S_m(x)$\u0000 with degree m. A local integro-sextic spline is constructed with the proposed algorithm. The local integro splines work efficiently, that is, they have low computational complexity, and they are effective for use in real time. The construction of nonlocal integro splines usually leads to solving a system of linear equations with band matrices, which yields high computational costs.","PeriodicalId":74944,"journal":{"name":"The ANZIAM journal","volume":"33 1","pages":"359 - 375"},"PeriodicalIF":0.0,"publicationDate":"2021-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84875214","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
ON MULTIFRACTIONALITY OF SPHERICAL RANDOM FIELDS WITH COSMOLOGICAL APPLICATIONS 球面随机场的多重分数性及其宇宙学应用
The ANZIAM journal Pub Date : 2021-04-18 DOI: 10.1017/S1446181122000104
P. Broadbridge, R. Nanayakkara, A. Olenko
{"title":"ON MULTIFRACTIONALITY OF SPHERICAL RANDOM FIELDS WITH COSMOLOGICAL APPLICATIONS","authors":"P. Broadbridge, R. Nanayakkara, A. Olenko","doi":"10.1017/S1446181122000104","DOIUrl":"https://doi.org/10.1017/S1446181122000104","url":null,"abstract":"Abstract This paper investigates spatial data on the unit sphere. Traditionally, isotropic Gaussian random fields are considered as the underlying mathematical model of the cosmic microwave background (CMB) data. We discuss the generalized multifractional Brownian motion and its pointwise Hölder exponent on the sphere. The multifractional approach is used to investigate the CMB data from the Planck mission. These data consist of CMB radiation measurements at narrow angles of the sky sphere. The results obtained suggest that the estimated Hölder exponents for different CMB regions do change from location to location. Therefore, the CMB temperature intensities are multifractional. The methodology developed is used to suggest two approaches for detecting regions with anomalies in the cleaned CMB maps.","PeriodicalId":74944,"journal":{"name":"The ANZIAM journal","volume":"12 1","pages":"90 - 118"},"PeriodicalIF":0.0,"publicationDate":"2021-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72871704","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
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