Analysis of New RBF-FD Weights, Calculated Based on Inverse Quadratic Functions

<div>Absolute value of local truncation error <svg height="9.25202pt" id="M153" style="vertical-align:-3.29111pt" version="1.1" viewbox="-0.0498162 -5.96091 10.4809 9.25202" width="10.4809pt" 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="M401 397C401 420 368 448 302 448C245 448 169 416 122 377C62 327 23 254 23 169C23 45 83 -12 181 -12C252 -12 323 29 374 85L358 107C305 62 257 43 210 43C147 43 110 98 110 189V214L313 208L321 256L115 250C132 342 190 405 253 405C291 405 323 389 346 360C356 348 364 348 377 357C392 367 401 384 401 397Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,5.187,3.132)"><path d="M504 89L488 119C453 85 428 69 416 69C408 69 405 75 412 102L462 304C492 438 460 451 436 451S388 441 356 423C311 397 229 336 170 256H168L189 340C208 418 200 451 177 451C144 451 82 413 24 352L40 322C65 345 98 369 108 369C114 369 119 363 112 335L28 -3L36 -12C54 -3 83 4 112 10C125 73 138 122 153 174C205 258 328 382 376 382C395 382 399 369 384 305L330 93C312 25 323 -12 351 -12C378 -12 439 21 504 89Z"></path></g></svg> for the IQ-RBF-FD approximation of <svg height="11.6425pt" id="M154" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -11.4361 13.9662 11.6425" width="13.9662pt" 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="M515 96L502 119C471 88 431 62 423 62C416 62 411 70 417 101C440 223 469 341 497 448H486L412 422L380 277C330 188 210 57 152 57C137 57 126 69 139 124L195 366C210 431 205 448 182 448C155 448 89 413 23 350L36 326C73 354 103 376 112 376C118 376 118 365 113 340L61 118C54 90 52 68 52 51C52 0 75 -12 98 -12S151 -3 181 17C242 58 305 119 362 193H364L345 104C323 3 339 -12 359 -12C390 -12 464 35 515 96Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,6.994,-5.741)"><path d="M310 541L304 571C290 586 211 619 185 610L80 76L131 52L310 541Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,10.033,-5.741)"><path d="M310 541L304 571C290 586 211 619 185 610L80 76L131 52L310 541Z"></path></g></svg> as function of <svg height="6.1673pt" id="M155" style="vertical-align:-0.2063904pt" version="1.1" viewbox="-0.0498162 -5.96091 5.39742 6.1673" width="5.39742pt" 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="M383 397C383 424 344 448 299 448C244 448 172 409 132 375C66 319 23 227 23 146C23 42 74 -12 146 -12C208 -12 298 30 359 103L343 124C315 95 248 48 192 48C145 48 111 85 111 163C111 228 129 294 151 330C171 363 201 401 241 401C275 401 302 384 325 356C332 347 339 344 348 348C373 360 383 381 383 397Z"></path></g></svg> using structured stencils with <span class="nowrap"><svg height="11.5564pt" id="M156" style="vertical-align:-2.26807pt" version="1.1" viewbox="-0.0498162 -9.28833 45.6445 11.5564" width="45.6445pt" xmlns="http://www.w3.org/2000/svg" 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Journal of Mathematics

fig2

Figure 2

Figure 2: Analysis of New RBF-FD Weights, Calculated Based on Inverse Quadratic Functions 