Computational and Mathematical Methods最新文献

{"title":"Solving Eikonal equation in 2D and 3D by generalized finite difference method","authors":"Eduardo Salete,&nbsp;Jesús Flores,&nbsp;Ángel García,&nbsp;Mihaela Negreanu,&nbsp;Antonio M. Vargas,&nbsp;Francisco Ureña","doi":"10.1002/cmm4.1203","DOIUrl":"10.1002/cmm4.1203","url":null,"abstract":"<p>In this article we propose an implementation, for irregular cloud of points, of the meshless method called generalized finite difference method to solve the fully nonlinear Eikonal equation in 2D and 3D. We obtain the explicit formulas for derivatives and solve the system of nonlinear equations using the Newton–Raphson method to obtain the approximate numerical values of the function for the discretization of the domain. It is also shown that the approximation of the scheme used is of second order. Finally, we provide several examples of its application over irregular domains in order to test accuracy of the scheme, as well as comparison with order numerical methods.</p>","PeriodicalId":100308,"journal":{"name":"Computational and Mathematical Methods","volume":"3 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/cmm4.1203","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84622658","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Pricing passport option using higher order compact scheme","authors":"Ankur Kanaujiya,&nbsp;Siddhartha P. Chakrabarty","doi":"10.1002/cmm4.1204","DOIUrl":"10.1002/cmm4.1204","url":null,"abstract":"<p>Higher order compact scheme (HOC) is used for pricing both European and American type passport option. We consider the problem for two different cases, namely, the symmetric case (which has a closed form solution) and the non-symmetric case. For the symmetric case HOC schemes result in slightly improved results as compared to the classical Crank–Nicolson implicit method, while still giving approximately second order convergence rate. In order to improve the convergence rate, grid stretching near zero accumulated wealth is introduced in the HOC schemes. The consequent higher order compact scheme with grid stretching gives better results with the rate of convergence being close to third order. For non-symmetric case we also observe similar results for both European and American type passport option. In absence of any analytic formula for the non-symmetric case, convergence rate was calculated using double-mesh differences.</p>","PeriodicalId":100308,"journal":{"name":"Computational and Mathematical Methods","volume":"3 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/cmm4.1204","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80500256","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"An asymptotic streamline diffusion finite element method for singularly perturbed convection-diffusion delay differential equations with point source","authors":"Senthilkumar Sethurathinam,&nbsp;Subburayan Veerasamy,&nbsp;Rameshbabu Arasamudi,&nbsp;Ravi P. Agarwal","doi":"10.1002/cmm4.1201","DOIUrl":"https://doi.org/10.1002/cmm4.1201","url":null,"abstract":"<p>In this article, we presented an asymptotic SDFEM for singularly perturbed convection diffusion type differential difference equations with point source term. First, the solution is decomposed into two functions, among them one is the solution of delay differential equation and other one is the solution of differential equation with point source. Furthermore, using the asymptotic expansion approximation, the delay differential equation is modified as a nondelay differential equations. Streamline diffusion finite element methods are applied to approximate the solutions of the two problems. We prove that the present method gives an almost second-order convergence in maximum norm and square integrable norm, whereas first-order convergence in <math>\u0000 <mrow>\u0000 <msup>\u0000 <mrow>\u0000 <mi>H</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mn>1</mn>\u0000 </mrow>\u0000 </msup>\u0000 </mrow></math> norm. Numerical results are presented to validate the theoretical results.</p>","PeriodicalId":100308,"journal":{"name":"Computational and Mathematical Methods","volume":"3 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/cmm4.1201","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"137812567","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Cyclic generalized iterated function systems","authors":"Rajan Pasupathi,&nbsp;Arya Kumar Bedabrata Chand,&nbsp;María Antonia Navascués,&nbsp;María Victoria Sebastián","doi":"10.1002/cmm4.1202","DOIUrl":"10.1002/cmm4.1202","url":null,"abstract":"&lt;p&gt;In this article, we introduce the notion of cyclic generalized iterated function system (GIFS), which is a family of functions &lt;math&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;f&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;f&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mn&gt;2&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;…&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;f&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;M&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;:&lt;/mo&gt;\u0000 &lt;msup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;X&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;k&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msup&gt;\u0000 &lt;mo&gt;→&lt;/mo&gt;\u0000 &lt;mi&gt;X&lt;/mi&gt;\u0000 &lt;/mrow&gt;&lt;/math&gt;, where each &lt;math&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;f&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;i&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;/mrow&gt;&lt;/math&gt; is a cyclic generalized &lt;math&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;φ&lt;/mi&gt;\u0000 &lt;/mrow&gt;&lt;/math&gt;-contraction (contractive) map on a collection of subsets &lt;math&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msubsup&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;{&lt;/mo&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;B&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;j&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msub&gt;\u0000 &lt;mo&gt;}&lt;/mo&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;j&lt;/mi&gt;\u0000 &lt;mo&gt;=&lt;/mo&gt;\u0000 &lt;mn&gt;1&lt;/mn&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;/msubsup&gt;\u0000 &lt;/mrow&gt;&lt;/math&gt; of a complete metric space &lt;math&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mo&gt;(&lt;/mo&gt;\u0000 &lt;mi&gt;X&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;d&lt;/mi&gt;\u0000 &lt;mo&gt;)&lt;/mo&gt;\u0000 &lt;/mrow&gt;&lt;/math&gt; respectively, and &lt;math&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;k&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;M&lt;/mi&gt;\u0000 &lt;mo&gt;,&lt;/mo&gt;\u0000 &lt;mi&gt;p&lt;/mi&gt;\u0000 &lt;/mrow&gt;&lt;/math&gt; are natural numbers. When &lt;math&gt;\u0000 &lt;mrow&gt;\u0000 &lt;msub&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;B&lt;/mi&gt;\u0000 &lt;/mrow&gt;\u0000 &lt;mrow&gt;\u0000 &lt;mi&gt;j&lt;/mi&gt;\u0000 &lt;/mr","PeriodicalId":100308,"journal":{"name":"Computational and Mathematical Methods","volume":"3 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/cmm4.1202","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90098401","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Evolution algebras whose evolution operator is a homomorphism","authors":"Desamparados Fernández-Ternero,&nbsp;Víctor Manuel Gómez-Sousa,&nbsp;Juan Núñez-Valdés","doi":"10.1002/cmm4.1200","DOIUrl":"10.1002/cmm4.1200","url":null,"abstract":"<p>This article deals with the evolution operator of evolution algebras. We give a theorem that allows to characterize these algebras when this operator is a homomorphism of algebras of rank <math>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 <mo>−</mo>\u0000 <mn>2</mn>\u0000 </mrow></math> and this result in turn allows us to extend the classification of this type of algebras, given in a previous result by ourselves in 2021, up to the case of dimension 4. For this purpose, we analyze and make use of an algorithm for the degenerate case. A computational study of the procedure is also made.</p>","PeriodicalId":100308,"journal":{"name":"Computational and Mathematical Methods","volume":"3 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/cmm4.1200","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82876915","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Quantum approximate optimization of the coset leader problem for binary linear codes","authors":"Markel Epelde,&nbsp;Elías F. Combarro,&nbsp;Ignacio F. Rúa","doi":"10.1002/cmm4.1196","DOIUrl":"10.1002/cmm4.1196","url":null,"abstract":"<p>The security of a broad family of coding-based cryptographic techniques relies on the hardness of the Syndrome Decoding Problem (SDP). In this problem, the aim is to find a word with a given syndrome and of Hamming weight smaller than a prefixed bound. If this last condition is replaced by “of minimum weight,” then we have the Coset Leader Problem (CLP), being Finding Low Weight Codewords (FLWC) a particular case (when the zero syndrome is considered). An algorithm that has been proposed in order to obtain approximate solutions of problems of these kind (NP-complete) is the Quantum Approximate Optimization Algorithm (QAOA), a variational hybrid quantum-classical algorithm. In this paper, we apply the QAOA to the CLP for binary linear codes. We model the problem, make the theoretical analysis the case of the first level, and introduce some experiments to test its performance. The experiments have been carried out on quantum computer simulators with codes of different lengths and QAOA of different depth.</p>","PeriodicalId":100308,"journal":{"name":"Computational and Mathematical Methods","volume":"3 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/cmm4.1196","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83121329","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A qualitative analysis of a Mycoplasma genitalium epidemiological\u0000 model","authors":"Ricardo Almeida,&nbsp;M. Teresa T. Monteiro,&nbsp;Ezio Venturino,&nbsp;Luís Machado","doi":"10.1002/cmm4.1199","DOIUrl":"10.1002/cmm4.1199","url":null,"abstract":"<p>The objective of the article is to present a qualitative analysis of a mathematical model for the spread of a sexually transmitted infection caused by <i>Mycoplasma genitalium</i>. Recent investigations revealed that this pathogen is becoming resistant to the use of macrolides and can turn into a superbug in the next few years. We present an epidemiological model to describe the spread of the disease. The equilibrium points are computed, and their local and global stability are studied. In order to make the mathematical problem more realistic, we propose two different optimal control problems that establish a balance between the number of infected individuals and the use of macrolides. Several numerical illustrations regarding the solutions of the proposed problems will be provided.</p>","PeriodicalId":100308,"journal":{"name":"Computational and Mathematical Methods","volume":"3 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/cmm4.1199","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79841094","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Qualitative behavior of a two-dimensional discrete-time prey–predator model","authors":"Messaoud Berkal,&nbsp;Juan F. Navarro","doi":"10.1002/cmm4.1193","DOIUrl":"10.1002/cmm4.1193","url":null,"abstract":"<p>In this article, we discuss the qualitative behavior of a two-dimensional discrete-time prey–predator model. This system is the result of the application of a nonstandard difference scheme to a system of differential equations for a prey–predator model including intraspecific competition of prey population. In particular, we evaluate the fixed points of the system and study their local asymptotic stability. We also prove the existence of a Neimark–Sacker bifurcation.</p>","PeriodicalId":100308,"journal":{"name":"Computational and Mathematical Methods","volume":"3 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/cmm4.1193","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74346265","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Computation of the reverse generalized Bessel polynomials and their zeros","authors":"T. Mark Dunster,&nbsp;Amparo Gil,&nbsp;Diego Ruiz-Antolín,&nbsp;Javier Segura","doi":"10.1002/cmm4.1198","DOIUrl":"10.1002/cmm4.1198","url":null,"abstract":"<p>It is well known that one of the most relevant applications of the reverse Bessel polynomials <math>\u0000 <mrow>\u0000 <msub>\u0000 <mrow>\u0000 <mi>θ</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 </msub>\u0000 <mo>(</mo>\u0000 <mi>z</mi>\u0000 <mo>)</mo>\u0000 </mrow></math> is filter design. In particular, the poles of the transfer function of a Bessel filter are basically the zeros of <math>\u0000 <mrow>\u0000 <msub>\u0000 <mrow>\u0000 <mi>θ</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 </msub>\u0000 <mo>(</mo>\u0000 <mi>z</mi>\u0000 <mo>)</mo>\u0000 </mrow></math>. In this article we discuss an algorithm to compute the zeros of reverse generalized Bessel polynomials <math>\u0000 <mrow>\u0000 <msub>\u0000 <mrow>\u0000 <mi>θ</mi>\u0000 </mrow>\u0000 <mrow>\u0000 <mi>n</mi>\u0000 </mrow>\u0000 </msub>\u0000 <mo>(</mo>\u0000 <mi>z</mi>\u0000 <mo>;</mo>\u0000 <mi>a</mi>\u0000 <mo>)</mo>\u0000 </mrow></math>. A key ingredient in the algorithm will be a method to compute the polynomials. For this purpose, we analyze the use of recurrence relations and asymptotic expansions in terms of elementary functions to obtain accurate approximations to the polynomials. The performance of all the numerical approximations will be illustrated with examples.</p>","PeriodicalId":100308,"journal":{"name":"Computational and Mathematical Methods","volume":"3 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/cmm4.1198","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80662524","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Controlling crop pest with a farming awareness based integrated approach and optimal control","authors":"Teklebirhan Abraha,&nbsp;Fahad Al Basir,&nbsp;Legesse Lemecha Obsu,&nbsp;Delfim F. M. Torres","doi":"10.1002/cmm4.1194","DOIUrl":"10.1002/cmm4.1194","url":null,"abstract":"<p>We investigate a mathematical model in crop pest controlling, considering plant biomass, pest, and the effect of farming awareness. The pest population is divided into two compartments: susceptible pests and infected pests. We assume that the growth rate of self-aware people is proportional to the density of susceptible pests existing in the crop arena. Impacts of awareness are modeled through the usual mass action term and a saturated term. It is further assumed that self-aware people will adopt chemical and biological control methods, namely, integrated pest management. Bio-pesticides are costly and require a long-term process, expensive to impose. However, if chemical pesticides are introduced in the farming system along with bio-pesticides, the process will be faster as well as cost-effective. Also, farming knowledge is equally important. In this article, a mathematical model is derived for controlling crop pests through an awareness-based integrated approach. In order to reduce the negative effects of pesticides, we apply optimal control theory.</p>","PeriodicalId":100308,"journal":{"name":"Computational and Mathematical Methods","volume":"3 6","pages":""},"PeriodicalIF":0.0,"publicationDate":"2021-09-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/cmm4.1194","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90225059","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}