Solving the Helmholtz Equation Together with the Cauchy Boundary Conditions by a Modified Quasi-Reversibility Regularization Method

<div>The variations of the system of equations (<a href="https://static.hindawi.com/articles/jmath/volume-2022/5336305/figures/#EEq25">42</a>) and the solution of the regularized system of equations (<a href="https://static.hindawi.com/articles/jmath/volume-2022/5336305/figures/#EEq12">12</a>)–(<a href="https://static.hindawi.com/articles/jmath/volume-2022/5336305/figures/#EEq12">15</a>) for <span class="nowrap"><svg height="11.7782pt" id="M142" style="vertical-align:-3.42938pt" version="1.1" viewbox="-0.0498162 -8.34882 29.0242 11.7782" width="29.0242pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M570 304C570 398 525 448 414 448C385 448 343 445 312 434L329 511L321 518C297 504 262 482 244 460L233 411C195 397 159 381 128 358L135 332C160 347 189 360 224 373L111 -147C97 -210 84 -218 17 -231L13 -257L254 -247L259 -218L233 -216C183 -212 177 -202 189 -142L218 -1C238 -10 266 -12 283 -12C351 3 429 48 483 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Journal of Mathematics

fig14

Figure 14

Figure 14: Solving the Helmholtz Equation Together with the Cauchy Boundary Conditions by a Modified Quasi-Reversibility Regularization Method 