{"id":595804,"date":"2017-10-20T02:00:00","date_gmt":"2017-10-19T23:00:00","guid":{"rendered":"http:\/\/www.fyysika.ee\/?guid=c37ae2bda17f9ae70c9d3631707d702b"},"modified":"2017-10-20T02:00:00","modified_gmt":"2017-10-19T23:00:00","slug":"solving-the-linear-inviscid-shallow-water-equations-in-one-dimension-with-variable-depth-using-arecursion-formula","status":"publish","type":"post","link":"https:\/\/www.fyysika.ee\/?p=595804","title":{"rendered":"Solving the linear inviscid shallow water equations in one dimension, with variable depth, using a\r\nrecursion formula"},"content":{"rendered":"<p>When solving the linear inviscid shallow water equations with variable depth in one dimension using<br \/>\nfinite differences, a tridiagonal system of equations must be solved. Here we present an approach,<br \/>\nwhich is more efficient than the commonly used numerical method, to solve this tridiagonal system of<br \/>\nequations using a recursion formula. We illustrate this approach with an example in which we solve<br \/>\nfor a rectangular channel to find the resonance modes. Our numerical solution agrees very well with<br \/>\nthe analytical solution. This new method is easy to use and understand by undergraduate students, so<br \/>\nit can be implemented in undergraduate courses such as Numerical Methods, Lineal Algebra or<br \/>\nDifferential Equations.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>When solving the linear inviscid shallow water equations with variable depth in one dimension using<br \/>\nfinite differences, a tridiagonal system of equations must be solved. Here we present an approach,<br \/>\nwhich is more efficient than the commonly used nume&#8230;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_genesis_hide_title":false,"_genesis_hide_breadcrumbs":false,"_genesis_hide_singular_image":false,"_genesis_hide_footer_widgets":false,"_genesis_custom_body_class":"","_genesis_custom_post_class":"","_genesis_layout":"","footnotes":""},"categories":[178],"tags":[],"class_list":{"0":"post-595804","1":"post","2":"type-post","3":"status-publish","4":"format-standard","6":"category-rss-fuusikaharidus","7":"entry"},"_links":{"self":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts\/595804","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=595804"}],"version-history":[{"count":0,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=\/wp\/v2\/posts\/595804\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=595804"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=595804"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.fyysika.ee\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=595804"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}